Photographing fireworks can be as easy or as hard as you want it to be. You will need a tripod, or some way to stabilize your camera to get good firework shots. Most cameras, even point and shoots, have a fireworks scene mode. Go your scenes on your camera, and find the firework icon. This will automatically set you camera at a slow shutter speed without a flash, ready to capture the fireworks. You will need to change your camera off this setting before photographing anything else.
If you want to set your camera settings all yourself, first turn off your on camera flash. I always shoot with the lowest ISO possible, so turn off your auto setting here. If you put it on auto, it will probably select a higher ISO to compensate for the dark night and it doesn't need to, fireworks are bright. If you have no idea what ISO is, just skip this, it is just detail work. The thing you want to focus on the most is shutter speed, you want a slow shutter speed. This is where it is necessary to have your tripod. Not matter how still you think you can hold your arms, they still shake. On a long shutter speed your camera is going to pick up on those small motions and your picture will be blurry. I have braced my camera on my knees while sitting down and it works OK, but a tripod really is best. You want your shutter speed to be about a couple of seconds. This is long enough to capture the full explosion of the firework.
The first fireworks make the best photos. For starters, there isn't as much smoke in the sky and there is only a few going at a time. It seems like the grand finale would make the best photos, but not so, you usually end up with really bright spots in the finale, like the photo below, because there are so many fireworks going at the same time.