[UPDATE: I added all the fireworks pictures I took here.]
Tonight I went to the Fair St. Louis fireworks show for Independence Day, and it was my first year with a DSLR and some proper lighting knowledge, so I had some fun taking pictures and trying to get some nice shots of the displays behind the St. Louis Arch.
Following techniques I've read about on various websites and forums, I set my camera on my sturdy Bogen/Manfrotto tripod, set the exposure to f/18, the shutter to 10 seconds, and the ISO to 200, then used my hand to let the camera know when to let in light. I would have my hand over the lens, press the shutter release button, then when I noticed a firework start, I would quickly remove my hand. Once one or two fireworks exploded and the trails were fading, I would quickly return my hand to cover the lens. This makes sure there aren't tons of fireworks over one area (which would create a washed-out frame).
I used the tripod because I needed a long shutter speed, and I used the small (f/18) aperture to make sure the flaming light trails from the fireworks would still show color. A lot of people leave their cameras in auto mode, with flash on, and their pictures turn out very disappointingly black (or they have little dots of fireworks on them). Switching into manual mode should solve this problem, if you follow the method I outlined above.