Disclaimer - I am not a doctor. The below is, however, from my own personal experience; of course, your mileage may vary.
I've found the traditional treatments (pumice stones, weird creams, and so on) to be ineffective. I had my wart treated with liquid nitrogen.
The procedure is thus:
Find a doctor that is able to perform this kind of treatment. (It isn't available everywhere but my university doctor had an easy supply of liquid nitrogen from the nearby physics department).
The doctor dips a (ahem) stick thing into a flask of really seriously cold liquid nitrogen.
You hold out your hand and try not to look too nervous.
The doctor gently applies the end of the stick to the wart. This really bloody hurts. There is a faint sizzling sound for a few seconds and you try not to scream, because after all the doctor still has the open flask of liquid nitrogen and you don't want to startle him.
The doctor takes the stick away, and sends you on your way. At this point the wart is an alarmingly bright yellow.
A few hours later, your hand finally stops hurting.
Over the next twelve(ish) hours the wart turns black.
Over the next day or two, it hardens and becomes a scab.
Eventually, it falls off, or more likely, you pick it off.
Underneath, hopefully, there is fresh pink wart-free skin. If it was a very large wart, there may be some remnants (i.e. a much smaller wart). In this case, you can return for another treatment.
In my (admittedly very limited) experience, it would have to be one seriously damned huge wart to need more than two treatments.
So, in summary, it really hurts (although see the updates below), but not for very long, and is totally devastatingly effective. The warts don't know what hit them.
As for how it works, the doctor told me that it's not quite as straightforward as the virus being killed by the low temperature. Supposedly, the human immune system is quite capable of fighting off the wart virus, but it doesn't have any reason to since it's not really harmful. Apparantly the 'attack' of the liquid nitrogen kicks the immune system into action, and so if you have several warts you may only need the freeze treatment on one of them in order to convince the immune system that 'warts aren't good' and have them all vanish. The doctor did indicate that this was theoretical; no doubt the world of medical research has more important things to be getting on with than proving this. (Rose Thorn informs me that a standard podiatrist treatment of cutting the wart and treating with acid or alkali works the same way.)
Maybe it isn't totally effective after all. My original treatment was back in 1998. Over the last week or so I've noticed the wretched wart is starting to reappear. I will be heading back for more freeze-therapy I fear.
I went for my re-treatment today, at a different surgery, since I've moved house since my original treatment. This time the doctor had some kind of advanced applicator tool, rather than the rather low-tech cotton-bud I'd experienced before. The new tool was much more precise, enabling the doctor to only freeze the affected area. It was much less painful - it still hurt, but it was nothing like as bad as before. There was no unsettling sizzling noise either. I have to wait a few weeks to see if it's been effective though, apparantly.
Update 2003 (whoops, forgot about this)
It took a few treatments but I'm all better now.