Late afternoon, Tuesday 12 January, the Caribbean. The sun is subsiding in the west, and, for some, it's lazy time. On his terrace in Santiago de Cuba, Eduardo Machin is sitting on a lounger, and down at the US base on Guantanamo Bay, it's towards the end of a nothing-special kind of day.

Some 160 miles across the sea, soldiers are patrolling more purposefully. They're part of the 11,000-strong UN force whose task is to bring some semblance of stability to Haiti, the land of voodoo, gang-law dictators and poverty so dire that three-quarters of these, the poorest people in the Western hemisphere, live on less than £1.30 a day. Yet, street by street, bit by corrupted bit, small victories are being won by the UN and aid agencies. And that's why, as the sun dips a little lower, and the clocks in Haiti's capital, Port-au-Prince, nudge round to 4.30pm, it has the feel, even here, of just another Tuesday.

At a college in the Morne Hercule area, Alex Georges is in a meeting with 30 other students and their professor. At an orphanage outside the capital, Susan Westwood, a nurse from Scotland, is tending children. Over at Notre Dame Cathedral, the Archbishop of Port-au-Prince, Mgr Joseph Serge Miot, is in his office, working at his papers. Jillian Thorp, an American aid worker, is at home in the capital, looking forward to her husband's return from a trip up country. In Haiti's parliament building, senate president Kelly Bastien is at his post; the white presidential palace, looking like a pavilion that's just come out of the wash, gleams across its watered lawns; US reporter Jonathan M Katz potters at home – after all, there's nothing much happening in Haiti at the moment. And, at the 12-storey UN headquarters, the head of the mission, Hedi Annabi, and more than a hundred of his staff are coming to the end of the working day. They have authority here. But not as much, it's about to turn out, as the geology on which Haiti sits.

A sudden lurch

The Caribbean Plate progresses, on average, at the sedate pace of 2cm a year. But, late this Tuesday afternoon, it takes a sudden lurch. In Guantanamo Bay, it feels as if a strong wind is blowing against the walls. Elsewhere in Cuba, Eduardo Machin is tipped from his chair. He is fortunate. He is more than 400 miles from the seat of the tremor – a wholly inadequate word suggesting nothing more threatening than the quiver of a pensioner's hand. In Port-au-Prince, no more than a 15-minute drive from the epicentre, things are different. At 4.53pm, a force 35 times more powerful than the Hiroshima bomb hits this poor, jerry-built city, giving it no more chance of surviving intact than the fragile toy of a bad-tempered child.

The quake lasts about 30 seconds, and, when it has finished, the landscape, and the lives of the two million people who inhabit it, are transformed – many by the crude expedient of being abruptly terminated. For those who survive, it must feel as if they've been mugged by God.

A few of the numberless dead had been sitting in the classroom with Alex Georges. The building shook, and then folded, killing 11. He survived, and was later found in the car park of the Hotel Villa Creole, now being used as an emergency dressing station. He lay under a "tent" made from bloody sheets. "I can't take it any more. My back hurts too much," he said, as he waited for treatment more than a day after the quake struck. At Susan Westwood's orphanage, "the wall started to shake and the floors were shaking. Things were falling off of the shelves. We heard glass shattering. And really it seemed to go on for maybe 40 seconds. It was terrifying… babies were crying, the Haitian staff were terrified. They were hysterical." At reporter Jonathan Katz's home "the house started to shake. Then it really started shaking. I walked out of my room and kneeled slowly to the undulating floor, laptop in hand, as windows, two years' worth of Haitian art and a picture of my grandfather smashed around me." But, at the UN's HQ, not one of the hundred-plus people inside emerged to tell how it disintegrated. It would be two days before one of them, an Estonian security guard, was pulled from the ruins alive. And, in the ruins of the archdiocese office, missionaries eventually found the crushed body of Mgr Joseph Serge Miot, their archbishop.

For nearly a quarter of an hour after the first great shock subsided, the city was obscured in a grey pall of dust from the disintegration of buildings made from cheap cement. There was smoke, too, as fires, both great and small, broke out. And, from everywhere inside this miasma, came screams and howlings, and alarm systems stuck in a piercing groove. But no sirens. No wail of emergency services; just the keening of a people left helpless.

As visibility returned, so the scale of it all (a scale so great, no Richter could reflect its impact) started to become apparent. The ornate National Palace crumbled into itself and now looked, with its white domes and fancy porticos broken and askew, like some ill-made wedding cake. The headquarters of the UN peacekeeping mission simply collapsed, as if it had been designed to do so. So did the Hotel Montana. Gone, too, were the twin spires of the Notre Dame d'Haiti cathedral. The main prison cracked open, releasing some of its dazed inmates. In Delmas Road, a major thoroughfare in the city, there were, as in many streets, more buildings fallen than standing. Homes and buildings that, minutes before, had stood on hillsides, were now so much scrap at the bottom of ravines. And under this new city of rubble, crushed to death, broken-limbed and pinned down by masonry, or remarkably unscathed but still trapped in the sudden darkness by great shards of stone they could not move, were perhaps 100,000 people.

Into the streets came the living

And, into the streets, came the living, although many of them did not look as if they were. Black faces were grey, and some bloodied – the undead resembling the dead, as they wandered about, shocked and, in every literal sense, helpless. Some screamed "Jesus! Jesus!" and ran in all directions. Others carried the bloodied bodies of children, relatives, friends, or someone they'd simply been with when the quake began. Some attempted to scrabble at the wreckage with bare hands, knowing that underneath it all was a loved one. At a destroyed four-storey apartment building, a girl of about 16 stood atop a car, trying to peer inside while several men pulled at a foot sticking from rubble. The girl said her family was inside. She was on her own. Everyone was now on their own. There were still no sirens, no police, fire, ambulances, power, phones, passable roads, paramedics anywhere to be seen. "At this point," said Alain Denis, a resident of Thomassin, just outside the city, "everything is a rumour".

People with satellite or other devices of the privileged, bureaucrats and agency journalists whose trade is level-headed facts, wrote things that would, in any other context, sound hysterical. Katz of Associated Press filed: "The city is a ruin. Fuel, food and water are running in short supply. Mothers have lost their children. Children have lost their families.

Entire neighbourhoods are sleeping in the streets. People walk miles up and down mountains, carrying everything they own, with no real place to go." And Michele Montas, former spokeswoman for the UN Secretary-General, Ban Ki-moon, wrote in an email to its New York headquarters: "Port-au-Prince is 80% destroyed… Saw hundreds of bodies in the street this morning and people trying to reach survivors under buildings and carrying the wounded on doors and makeshift stretchers. Most everything above one-storey has been levelled."

Every so often, the geology that caused all this reminded the city it was still there, grinding away, five miles below. Aftershocks came with such frequency that, by Thursday morning, the US Geological Survey had recorded 33. Thousands gathered in public squares, singing hymns and weeping; and they were not the only voices. Throughout the night, there were the echoing moans of the bereaved, and, softer but most plaintive of all, the cries from within the rubble of those still trapped. From under a collapsed kindergarten in the Canape Vert area, a woman beseeched anyone who might be passing: "Please take me out, I am dying. I have two children with me." And everywhere, people in shock. A woman sat outside a collapsed house. Her baby – dead – was laid out on what used to be the roof. "Do you see my baby?" she asked passers-by.

As Wednesday dawned, in small pockets of Port-au-Prince, 3,000 police and international peacekeepers tried to clear roads and direct the desperate traffic, but the task was overwhelming. "We just don't know what to do," a Chilean peacekeeper said. Some people fled, or tried to, balancing suitcases full of what they could rescue on their heads. An exodus began to the countryside, where the wood and cinderblock homes were too flimsy to have inflicted much damage when they collapsed. Many of these shacks survived.

Like a nuclear attack

All over the city, there were scenes resembling those in films depicting the scrabble for survival after a nuclear attack. In Petionville, people used sledgehammers and their bare hands to dig through a collapsed commercial centre, tossing aside mattresses and office supplies. Nearby, about 200 survivors, including many children, huddled in a theatre car park and used sheets to rig makeshift tents to shield themselves from the sun.

And when it had gone down again, in the frightening pitch black of Haiti's night, religious songs rose from groups of people huddled in open spaces for safety and solidarity. The chanting and clapping, mainly by women, echoed from hill to hill, street to street, as Haitians prayed for their dead. Foreigners slept around the hotel's pool while scores of injured and dying people lay outside. At the Oloffson, the hotel made famous by Graham Greene as the Trianon in The Comedians, manager and musician Richard Morse tweeted: "17:38 13 Jan: there is no police presence... there is no UN presence in the Carrefour Feuilles area... people are trying to take care of themselves."

Yet there were, amid the ruins, stories of remarkable escapes. A Canadian woman trapped under debris texted her country's foreign affairs department in Ottawa for help. The message was relayed to diplomats in Haiti, and she was duly rescued. And Jillian Thorp, an American aid worker, was pinned down for 10 hours in the wreckage of her mission house. But her husband Frank, up country at the time of the quake, drove 100 miles back to the capital, and dug for more than an hour to free her. Haitian senate president Kelly Bastien was rescued from the collapsed parliament building and taken to a hospital in the Dominican Republic.

Bodies piled on the streets

As Wednesday became Thursday, the bodies of the dead were still piled in the streets. Most were covered with sheets. Passers-by would stop, lift the corner of the covering, and peer to see if a loved one was underneath. Outside one crumbled building, the bodies of five children and three adults lay heaped up, like refuse awaiting collection. On many streets, alongside the dead lay the injured, waiting in agony for the help that may never come, their injuries fast turning infected. There were almost no ambulances, and few hospitals where the injured could be taken. At least eight were ruined, others had large parts out of action, and many aid agency facilities were also unusable.

The health centre of Médecins sans Frontières was damaged, and staff injured, but hundreds, lacking an alternative, still came. They scattered themselves around a courtyard, sleeping in tents, on top of rugs, on the floor and on plastic sheeting, waiting to be transferred to one of the two hospitals identified as safe enough to withstand the aftershocks. More than 500 people needed immediate surgery. Whether they would get it was another matter. Equipment was running low (they had no x-ray machines, surgeons or scalpels on Thursday), as was the petrol to transport patients, food and water. These were not the only problems. Large numbers of its 800 medical workers in Haiti hadn't been seen since Tuesday afternoon.

Cuba, which already had hundreds of doctors in Haiti, treated the injured in field hospitals, and the Hope for Haiti charity set up a mini-hospital outside the Villa Creole, where it tried to treat people for broken bones and internal bleeding. The charity's country director, Mike Stewart, said on Wednesday night: "Ten who have come to us have died already. There will be more dead by morning. We need to operate but we don't have the equipment." Neither did the US Red Cross, which said it was also running out of medical supplies. For several days, makeshift was the only health service available. Pick-up trucks became ambulances, and doors and wheelbarrows became stretchers. But there is no substitute for clean water. Veronique Taveau, spokeswoman for the UN children's fund, warned that, unless sufficient supplies of water came soon, survivors risked "all the diseases you can imagine" – dengue fever, malaria, measles and that great killer of disaster survivors – diarrhoea.

On Thursday, help began to arrive. Almost the first to land were the Chinese. More than 50 search-and-rescue specialists and medics barrelled out of a plane in orange jumpsuits, with dogs on leashes. They were all ready to go but, such was the damage at and around the country's airport, they couldn't get very far. Seventy-one experienced rescuers from Britain landed in the Dominican Republic, which shares the island of Hispaniola with Haiti, and travelled in by road through the early hours. They were in Port-au-Prince before midday. More teams followed, from France, Iceland, Spain, Canada, Israel, Germany, Mexico and Venezuela. They all had expertise. What few of them had was the heavy lifting equipment, and those that did had trouble getting it to where it was needed.

From the US, a massive response was dispatched. The US has done more than its fair share to destabilise Haiti. But recently, through former president Bill Clinton, its special envoy, and substantial financial assistance, it has begun to make amends. And, ordered by President Barack Obama, and steaming towards Haiti as fast as it could, was a flotilla of help: the nuclear-powered aircraft carrier USS Carl Vinson, three amphibious ships from the US Second Fleet, including the 844ft-long USS Bataan, which carried 2,000 Marines with helicopters, plus 8,000 troops. The first contingent, from the 82nd Airborne Division, was on the ground by Friday, and the rest should all be in action by tomorrow, but USS Comfort, a hospital ship with 12 operating rooms, will not arrive for a further five days. And there were, from around the world, those promises that do not always materialise in full: pledges of cash. From the World Bank, $100m (€69m) and the commitment to "consider" a reconstruction trust fund; a similar sum from the US; from Ireland €1.9m, Britain, €7m; and many more from around the world: Australia (€6.5m), Norway (€3.7m), Canada (€3.5m), Spain (€3m), Italy (€1m), India (€700,000) and Sweden (€590,000).

But, even on Friday, getting rescue and emergency medical help to those who needed it was proving, in the words of UN spokeswoman Elisabeth Byrs, a "logistical nightmare". The capital's port was damaged beyond immediate use, and such was the wretched state of Port-au-Prince airport that 11 aid flights were turned away on Thursday, and it took six hours to unload one commercial plane. By the end of the week, planes were packed on to tarmac so tightly that their wings overlapped. Nor was the airport connected to the city by a serviceable road. And so parts of the relief operation that no lay person ever considers became vital, such as the four volunteers from the British charity MapAction who arrived on Thursday. They use on-site information, the latest mapping technology and satellite imagery to update existing maps and show where bridges or roads are no longer usable, where survivors have gathered, and the most effective way to get through.

The UN decapitated

UN peacekeepers and aid workers did try to fill in holes and build temporary bridges, but this was an organisation which was decapitated on Tuesday when the quake killed its two senior officials, and hundreds of those serving with them. At least 140 members of its staff are still buried, presumed dead, under the rubble of its headquarters. Nor was there any functioning phone system, and the UN was working frantically with the independent aid agency Télécoms Sans Frontières to get some lines working again. There was still so much that was lacking, not least bodybags. Tens of thousands were flown in on Friday, but there were increasing signs they would not be enough. The Red Cross, after several days' assessment, was estimating that between 40,000 and 50,000 had been killed on Tuesday.

How many have died since is anyone's guess. There are many like the woman in her 20s who, for more than two days, lay wounded and suffering on a patch of dirt by a road junction until, late Thursday, she had no more breath to give. Her family gently wiped the corner of her mouth, closed her eyes, said a prayer and covered her with a blanket. Her father sat in some sort of vigil at her feet. He was asked her name. All he could do was shake his head.

By week's end, clearing corpses was a monstrous task. Some 7,000 had been buried in a mass grave outside the city, but this was a fraction of the bodies littering the streets, filling the air with a stench so bad that few could go far without covering their noses. People took relatives to nearby hills for impromptu burials, others brought them to the mortuary at Hospital General, already filled to overflowing with more than 1,500 rapidly decomposing bodies, many of which had been lying in the sun. No more than 20ft away the injured lay on mattresses. And, in the city centre, a photographer for Time magazine saw two roadblocks constructed from, among other materials that came to hand, dead bodies. Compared with these, the six dead, laid shoulder to shoulder under a dirty sheet on the steps of a pharmacy, have had a decent departure from this life. By the weekend, many streets and parks had been turned into makeshift hospitals and refugee camps, most of them corralled with piles of salvaged goods. There were reports of people raiding ruined shops for food. The accounts used the word "looting". "Surviving" might be more accurate.

Not everyone who lived through that first terrible geological tantrum will survive. This weekend perhaps one person should stand as their memorial. She is Haryssa Keem Clerge, and her home was in the Petionville area until, late on Tuesday afternoon, it collapsed into a ravine with her and her family inside. On Wednesday, Haryssa's mother was pulled from the rubble, wounded but alive.

Then, a little later, word went round the neighbourhood that Haryssa could be heard, crying and calling for rescue, from somewhere in the ruins. People rushed to help, and, after they'd scrabbled for hours, they found her. She was in what had been the basement, and had been pinned down by part of the roof for two days. Rescuers got close enough to give her water, but not food, and even as they told her to hang on she died. She was nine years old. Finally, they were able to free her body, wrap her in a green towel, and place her in the discarded drawer of a broken desk. It will almost certainly be her coffin.

Everywhere here this weekend there are Haryssas, and flies and the smell of decaying flesh. This, truly, is the land of the dead and the pitiful undead.