While dipping your hand in gasoline is one way to make flame appear from it another more mundane method is to use alcohol. What you'll need is a can of either strong beer or liquor and a lighter or match.

First, while nobody is looking splash your (alcoholic) drink over you hand. Then light it with you lighter and wave it around like a maniac (but not fast enough to put the fire out). From here you can either pretend your in horrible pain or play it cool, but it being alcohol it doesn't generate very much heat.

Another alternate idea is to pretend that nothing is happening while making sure everybody can see your hand. For best results do this in a darkened room or at night as alcohol flames aren't that bright.

In reply to the numerous comments saying that this won't work with beer, I personally have done this on many occasions. Strong beer is not even necessary if you're lucky, but it works best. The alcohol does light up and noticably too. However I won't recommend that you try it just to make sure it works though, as it might be riskier than I think it is. Just ask yourself what's more important to you, no risk of bandages or oohs and aahs.

I'm also told that doing this with spirits or pure alcohol could get you a trip to the emergency ward if it runs between you fingers, so be careful and start with small amounts first! BTW, if the above writeup about gasoline is still around please realise it's a joke. Even alcohol burns pretty hot, so just forget about petrol.