1. Find a steady place to rest your arm or place your camera. The hood of a car or the back of a chair is a good spot. You need to hold the camera extra still in order to get good fireworks pictures, so this is a must.
2. Turn off the flash. Fireworks and flash never go together.
3. Your camera might already have a mode that is labeled fireworks. Essentially, this setting will give you a low ISO with a three to four second shutter speed, which works well for this type of shot.
4. If your camera doesn't have a fireworks setting, look for a non-flash setting that favors Aperture. For example, the "A" on the dial.
If you're using a Digital SLR:
1. You can try finding a steady place to rest your arm, but ideally, use a tripod. The tripod will ensure that you can use long shutter speed without jiggle.
2. Use a remote control shutter release or the timer feature on your camera so you don't have to touch the camera and accidentally jiggle it.
3. If you own or have access to a wide angle lens, use it. It will also you to create a dynamic, soft shot. If you don't, that's OK, just be sure to use an aperture between f6 and f11.
4. Shoot in manual, flash off with a low ISO setting. Remember fireworks are very, very bright bursts of light. If you shoot at a high ISO, the black night sky will be very grainy. Think of the fireworks as your light source.
5. Don't be afraid to experiment. An out of focus shot will produce an interesting bokeh look.
6. If you're using a modern DSLR, try using all the settings above on video mode. Video of fireworks can be just as fun and it can make experimentation easy as you rotate the focus. It truly can produce some interesting results, as seen in this video below.
Whether you're using a point and shoot camera or a Digital SLR, remember to pick a location that has the potential to create an interesting shot and will work well for your specifications. If you're using a tripod, a sandy area might not be a great location, because it will be an uneven surface. Similarly, large street lights, posts and buildings can either be used to frame a shot OR can potentially ruin a shot because they'll be in the way.
Thinking ahead will ensure that you get a great shot worth framing.