Visit Amsterdam on Queen's Day, when the whole city changes colour, and you can either join the party or explore the empty museums. The only no-show is the monarch herself
The convicts waved from their narrow cell windows, using gestures that grew increasingly more explicit as the crowd cheered back. Normally, the offenders were denied an audience, because on every other day of the year, trains hurry along the railway line at the point where it passes the prison. But it was Queen's Day, and the express from Flushing had braked right alongside the barbed-wire-fringed monolith that looked like a fragment from a British university campus in the Eighties

The convicts waved from their narrow cell windows, using gestures that grew increasingly more explicit as the crowd cheered back. Normally, the offenders were denied an audience, because on every other day of the year, trains hurry along the railway line at the point where it passes the prison. But it was Queen's Day, and the express from Flushing had braked right alongside the barbed-wire-fringed monolith that looked like a fragment from a British university campus in the Eighties.

The driver did not pause because he wanted to peer at the inmates; he had been ordered to stop. Amsterdam's Central Station was so full of people that no more trains were being allowed in until the crowds had shifted. And on Queen's Day in Europe's most humane city, it's impossible to move faster than the slowest common denominator ­ which, in this case, was a muscular and hairy orange fairy on stilts.

I caught up with "her" later, beside Herengracht, the greatest of the semicircle of concentric canals dug in the 17th century that define the heart of Amsterdam. I was trying to steer a course through what, from the air, must have looked like an incredibly successful giant cobweb. About a million creatures, many of them dressed or daubed bright orange, were flapping around the strands of canals and bridges that comprise Amsterdam's seductive net. On closer inspection, though, the only adhesive was a sticky film of beer on the cobbles. The participants were being wildly patriotic, with the emphasis on wild.

Queen's Day, or Koninginnedag, is held each 30 April to celebrate the monarch's birthday. That's not strictly true. Last year, the final day of April was a Sunday, and sufficient godliness remains in Holland for cleanliness to rule on the Sabbath, so they moved the celebrations to 29 April. Neither date is anywhere near Queen Beatrix's birthday, which falls on the last day of January. That is a bitterly cold time of year in the Netherlands. So the birthday of the former queen, Juliana, is used instead, with the occasional modification to suit those among the religious-minded Dutch whose principles are not so flexible as to accept an orgy of smoking, drinking and commerce on a Sunday.

As far as I know, this frenzy of indulgence does not extend to the Royal Palace, whose awkward bulk on Dam Square betrays its municipal origins as the City Hall. But it is difficult to tell because Beatrix, Queen of the Netherlands, Princess of Orange Nassau and Countess of Holland, usually leaves town on her big day. Anyone who dares to be in Holland's capital on Queen's Day is royally inconvenienced.

The Dutch seem much more at ease than the British about royalty, perhaps because the Netherlands is really a republic that boasts a monarchy in the same way that a hat might sport a feather. The main axis of the Dutch royal family is the Nassau line, whose origins lie in Germany, but celebrants seize on the fact that, in 1544, Willen van Nassau assumed the title Prince of Orange. Real power, though, has long resided with merchants and citizens.

Gay couple in Amsterdam

A civic tolerance prevails. Amsterdam's red-light district brims with sex on sale, while last weekend, the first legal gay marriages took place. The city, long a haven for refugees, is deliciously multicultural. The apparent chauvinism of seizing on orange is a mask for celebrating the all-embracing nature of the Netherlands. As everyone revels in the glaring intersection between red and yellow, royalty turns a blind eye to the abuse of its honour, to the all-day street party and a city-wide flea market.

How could a royal event degenerate ­ or improve ­ to the point where a city is allowed to go noisily, collectively mad? Accounts differ. From the not-altogether-coherent ramblings of a number of people I blundered into, it appears that the first suspension of normal life was when citizens were allowed to sell whatever they wanted, wherever they wanted, during Queen's Day. No licence was required, and few questions of a legal nature were asked. It resembles a gigantic car boot sale, except without the cars. Trading is allowed between 6am and 9pm, though the police do not rush in to enforce closing time.

Many people use the opportunity to dispose of household junk, while more enterprising folk buy wholesale and were using the opportunity to turn a handy profit on 10 green bottles of Heineken or 100g of Lebanese red. Were it not for the fact that everyone is in far too good a mood, you might feel that you have stumbled into a congregation of homeless people.

Homelessness is a real risk for visitors. Increasingly frantic phone calls revealed that, of the city's stock of 32,000 beds, only one remained in the whole city. I had to get across to the Eben Haezer hostel straight away. It turned out to be an oasis of wholesomeness in a city where sin seems embedded as firmly as the 13,659 wooden piles on which the Royal Palace stands. The bed rate of £11 entitles you to a smoke and alcohol-free environment, with a wide selection of religious literature in a dozen languages, and optional Bible classes. I checked in then slipped out as soon as I could, to greet a city swaggering with pride and staggering with the effects of an ambition range of mind-amending substances.

So what exactly, as the Queen herself no doubt asks at official functions, do you do? You walk, and shop, and look. Even through a fug of people, Amsterdam is dazzlingly beautiful. The marsh on which the Dutch capital rests, unsteadily, has kept it a low-rise city. One thousand bridges provide a weft to the warp of 100 canals that ripple out from the medieval core of the city. For the perfect conjunction of water, architecture and tranquillity, make your way through the unholy Scrabble of an Amsterdam street map to the Eerste Leliedwarsstraat bridge over Egelantiersgracht in the Jordaan.

Unlike the Notting Hill Carnival or an Ulster parade, Koninginnedag consumes the whole core of the city with no undercurrent of aggression. Indeed, the swirl of humanity is underpinned by the bonhomie of a New Year's Eve celebration.

Any casual observer will see that the city is in turmoil, and conclude that there is no point in going to the big museums. Yet Queen's Day is the ideal time to sightsee. Many of the "real" tourists who normally fill Amsterdam's hotels are outbid by Dutch folk who are avowedly not here to see Impression: Painting Quickly in France 1860-1890 at the Van Gogh Museum; they are here to paint themselves and each other quickly, impressionistically, before plunging back into the swaying and the dancing.

So you can breeze around the Van Gogh and many of the other museums in this miraculous city, which was founded a millennium ago on the silt swept down the Rhine. Afterwards, pick your way to Spui, about the finest square in medieval Amsterdam. Take a coffee in the Art Nouveau Grand splendour of the Café Luxembourg, or help the barman at the legendary Hoppe "brown café" maintain his reputation of pumping more beer than any other bar of its size in Holland.

An anonymous doorway leads from the square into the Begijnhof, a cloister for the support and protection of women. During Queen's Day, the winsomely pretty ensemble maintains its principles and decorum. You may trespass on the quiet courtyard only between 10am and 5pm. But to seek sanctuary on a day like this is eccentric. Even to nip into a "coffee shop" and devote your day to sampling as much of the herbal menu as possible would be irrational.

Being outside, senses sharp, is the way to experience Queen's Day. Jazz bands drift past on the canals ­ waterways normally lined by sober 17th-century mansions topped with elaborate gables, but today enhanced by clowns and jugglers topped with orange plastic crowns.

Meanwhile, the odd orange fairy on stilts keeps a high-altitude eye on proceedings. A magic travel wand helps if you want to join in the civic jollity. I arrived on the not-so-express train from Flushing because all flights into Schiphol airport were booked. So I took a ferry from Dover, a ferry to Ostend, a train to Bruges, a bus over the border to Holland, a ferry across the river Scheldt to Flushing, then the train.

Next morning, I had to make the same journey in reverse, while the municipal patient recovered from her indulgence of the previous day. Amsterdam felt more sluggish than the dreariest Boxing Day in Britain. One place still sparkled, though: the Grand Café Restaurant 1e Klas, occupying the former First Class Waiting Room in the now-placid Central Station. At 9.30am, the neo-Gothic wonder opened, supplying a fresh Dutch breakfast before the Flushing Flyer departed.

The train flashed passed the jail, but no prisoners flashed back. As it clattered on towards Schiphol airport, a familiar aircraft fluttered past the window.

Of course, I thought, that's what the orgy of orange looked like: the intergalactic staff party for easyJet.

Simon Calder is co-author, with Fred Mawer, of the 'Spiral Guide to Amsterdam', published this week by AA Publishing, £9.99