As with most low-light photography, shooting a meteor shower definitely requires a tripod and shutter release cable or remote control (though you could also use the self-timer to eliminate camera shake). Make sure you charge your camera's battery fully before you go, and bring extras if you can. A fast, wide-angle lens is your best bet — 21mm f/2.8 or faster will give you the best results. Since there's no way to predict exactly where the meteors will fall, the wider your lens, the more sky you'll get in your photo and the higher the chance you'll catch a shooting star.
There are two schools of thought about ISO. Some say to use the highest ISO you can, so that you can use a shorter exposure time and thus eliminate star trails. But I've found that setting your ISO between 100 and 400 is the best combination of exposure times and less graininess. The faster your lens, the lower the ISO you can reasonably use. Use an aperture a stop or two up from the widest your lens will go; this will let you use a longer shutter speed without letting in too much ambient light.
Shutter speed math
The question of how long a shutter speed to use is somewhat complicated and requires a little bit of math. Don't worry, though — it's a simple equation!
The issue is that you want to use a slow enough shutter speed to capture a good number of meteors, but not so slow that the stars themselves appear as streaks. We all know the earth rotates, but it can be a bit surprising how little time it takes for that rotation to show up in our night sky photographs. For a very long exposure, this can be an intentional artistic choice; but usually for photos of meteors, we prefer that the stars appear as pinpoints of light, and the only streaks are those of the meteors themselves.
