It's a clear, shiny night. I'm sitting on a high balcony outside the National Theatre listening to music and watching blocks of flats career across the surface of one of the South Bank's concrete towers. Every now and then a passenger plane shimmers out of the clouds and disappears silently behind this huge, ad hoc movie screen.

The planes are real. The apartment blocks are part of a video installation that has been playing on the National Theatre fly tower. The Belly Button Like a Village Square - as Pipilotti Rist called her work - could be seen by theatregoers wandering around with their interval drinks, but also by anyone walking across Waterloo bridge between 8.30pm and 10.30pm in early October.

What are we - theatregoers, pedestrians and I - to make of this peculiar spectacle? We sit or stand for a few minutes as the scene changes from the swirling tower blocks to a glimpse into one of the flats, where a woman in a psychedelic dress is pushing her face against a window so that it smears out of shape, becomes just another jumble of shapes and colours. It looks a bit like a riff on Monet's Waterlilies, with plate glass standing in for a pond surface. It is oddly exhilarating.

Before I have time for any other thoughts, we're rattled off in a rather posh train dining car, peering out of the window as the countryside races past. Why is the train empty? It's chilly on the National's balcony, and I'm just about to go back indoors when, in the corner of the train window, I spot the reflection of a passenger. In a month of bingeing on video installations, I learn to look for this sort of shadowy figure - a reflection, a silhouette - which is more often than not an image of the artist.

After 20 minutes watching Belly Button, I have begun to make out five different scenes. It is starting to look a bit repetitive, but that is because it is repetitive. It's on a "loop", which is programmed to play again and again. You can come in at any point and watch for as long as you like.

This must be odd to the theatregoers with their interval drinks, who are in the middle of something with a beginning and an end. On the other hand, unlike more abstract video art, Belly Button does have scenes and it also has a woman performing - in a look-at-me, pop brat sort of fashion.

I take these thoughts off to London's Lisson Gallery, where there is a show by an up-and-coming Glaswegian artist Roddy Buchanan. Time Out says he is "known for elevating competitive games to an existential level where critical issues of nationhood and selfhood are set in play".

What I see is a series of rooms that look almost empty - as if workmen have knocked off for a tea break in the middle of putting up the show. In the first, some big black leather beanbags are ranged around a television screen that someone has left on its side. On the screen are a series of vertical tubes with kitsch scenes inside them, each with a plastic object trundling downward - a taxi in a New York street, perhaps, or a bear in a snowy forest. I'm baffled, until it is pointed out that these are in fact the sort of novelty pens that tourists buy. It is also pointed out that I am sitting on a punchbag which is made to the exact weight of a particular boxing champion at the moment of his defeat. I scuttle back to that Time Out review: "Competitive games, existential level". Ah.

The next work is simply beautiful. It's an aerial shot of the Tour de France: hundreds of cyclists looking like Damien Hirst dots pour up a screen that is also a road, funnelling themselves through roundabouts and spilling out on the straight. I could watch it forever, waiting for one of them to wobble and the whole lot to career out of control. Except that after a while they don't look like cyclists racing up a road, but a cake-maker's spillage of hundreds and thousands with chocolate icing pouring down past them.

This irreverent image prompts an irreverent thought: how did Buchanan make it? Surely he couldn't have staged his own Tour de France and hired his own helicopter to film it from?

Indeed, as gallery owner Nicholas Logsdail explains, he did not. The whole thing was recorded from Eurosport over 26 hours, and edited down to the only four minutes in which the cyclists were going up the screen. "It's the idea and the editing that are his," Logsdail tells me. "It's the only video piece where he has actually appropriated his material." For a moment I come over all moral. I mean, who actually owns this footage? Then I realise that it's not so different from Duchamp's urinal, the toilet with a place at Tate Modern.

Except that in several puzzling respects it is. The urinal is, crudely, an art object. Video art is, as one art critic put it, "some stuff in a plastic case". And it's not just confined to galleries: it has been commandeered by advertising and pop (one of the big names in video art, Chris Cunningham, made the video for the Prodigy's infamous Smack My Bitch Up). It's all around me and it's becoming increasingly clear that I know nothing about it. Where did it come from? How do I know when it's art?

In a fret, I ring the Guardian's art critic Adrian Searle, who tells me that I need to learn to distinguish between artist's video and artist's film, but that the distinction is "a porous thing". Video art, says Searle, comes from the US in the 1960s, where artists began to use video to make a record of performances, which were otherwise unrepeatable. Back in 1972, I discover, the Lisson was one of the first to show a work of video art in British galleries. It was by the American artist Dan Graham and was called Past Future Split Attention. It featured two students, one of whom could talk only about the past, while the other could talk only about the future. It's now regarded as a classic work, and you can get it out of a video art archive in New York.

So, this is an art form with its own documented history, but it's also so new that even the experts don't know exactly where it's going. Take the distinction between film art and video art. One difference seems to be that film produces higher quality pictures than the fuzzy, wobbly, homebody medium of video. My encyclopedia of art history says: "A key difference is that for the video artist the monitor is itself a visible part of the artwork." Nowadays, I'm told, some artists work on film because they like the quality of it, but then transfer it to video because that has certain other advantages: for instance, you can put it on a loop and show it on a monitor which becomes a visible part of the artwork.

The centrepiece of Roddy Buchanan's show - Catch 60'6" - isn't edited. The title refers to the distance between pitcher and catcher on a baseball diamond, and the screens are placed exactly that distance apart - as were camera and sportsman when it was filmed at a baseball club in Edinburgh. At first, standing between the screens, you just hear "thwack, thwack, thwack". Then the corner of your eye catches the fleeting image of a player catching a ball at one end of an otherwise black screen. Seconds later he does exactly the same at the other end. And so on. This is real time and real space, but it's also a video. Buchanan calls it his Waiting For Godot. Beckett, I discover, is the patron saint of video artists.

But Beckett didn't produce work for exhibition in galleries. He didn't belong to the strange commodified culture of the artist, who survives and thrives by selling work by the piece. Which brings me to the most delicate question: What exactly is a work like 60'6"? If someone were to buy it (as it is hoped they will), what exactly would they be buying? The answer, as with so many of the video works I see, is not only the film itself but also a set of instructions. In this case: "2 screen projections (5 min. loop) size of screens 97.5 x 130cm each. the screens must be 60'6" (18.47m) apart)."

You couldn't understand Catch 60'6" without knowing how to mount it any more than you could understand a Beckett dramaticule without the stage directions. Nor could you show it without a room long enough to take it.

So who might buy it? Probably a museum, but not always: there are a growing number of private collectors prepared to invest in video work even if they could never show it in their own home. "The beauty of video," says Logsdail, "is that you've got to look at it more in the way you'd look at collecting CDs." So you might have stacks of art on your shelves? What happens if your toddler spills Ribena all over it?

The scenario may be fanciful but the issue is not. The Tate's electronic conservation department has the job of looking after the collection of 80 or 90 video works that the gallery has built up since the late 1980s. It's a delicate business, says conservator Sarah Joyce, and quite different from looking after a famous painting. One of her jobs is to make sure that each work is available in a variety of formats: on video for researchers; on DVD for exhibitions and on very high quality tapes for the "archival master". This is the Big Daddy of tapes, except that in some cases the actual, physical original - the one with the artist's fingerprints on it - stays in the artist's possession.

Then there's the extra problem of formats becoming obsolete, and having have to be "refreshed". So it's a bit like ensuring that the diary you once kept isn't stuck on an Amstrad disc.

Towards the end of my video odyssey, I look in on Facts of Life at the Hayward Gallery. This show of new Japanese art includes one film of a workman patiently trying to get an electric drill to work though the cable is too short to reach the socket. Very Beckett.

Then there's a work called Then I Decided To Give a Tour of Tokyo to the Octopus from Akashi 2000, in which the artist does exactly what he promises, introducing his lump of tentacular jelly to everything from Mount Fuji to a fish market before putting it back in the sea. It's surreal and comic, but if I'd seen it on TV in one of those short film slots, it would never have occurred to me that it was an artist's video, just that it was a cheaply made short.

But I saw it in a gallery. The context is all. Here. But not always. Now there's a good title for a piece of video art.