Almost everyone enjoys a good fireworks show, especially photographers. Photographing fireworks can be a lot of fun regardless of your skill level. Since it is a lot like shooting lightning, except a lot safer, it helps me keep my shooting skills sharp. You can certainly capture images of fireworks with any camera, but you are going to have the best results with a tripod and camera that has a manual mode. For best results, a shutter release cable or wireless remote will come in handy to prevent camera shake.
First, you need to set your focus manually. In most cases, you are going to be far enough away from the fireworks that focusing out to infinity works just fine. This isn't always the case however. In the closeup shot at the top of this article, I was extremely close. I simply focused on the spot on the ground in which the fireworks were being launched. After seeing one or two fired, I then adjusted the camera angle for height.
You want to use a medium aperture, or f/stop setting. The initial instinct is to use a low f/stop since you are outside shooting at night, as you would shooting a meteor shower. This isn't necessary. On the contrary, it can cause your shots to be all white and wash out any color. I usually start at f/8 and adjust as I see fit from there. Also, I shoot fireworks at ISO 100 and leave it there. I will adjust the f/stop up or down as needed to compensate for the exposure I need.
Using a tripod & shutter cable, I normally place my camera in 'bulb" mode. This keeps the shutter open for as long as I keep the button depressed and closes as soon as I let go. The length of time you leave your shutter open can depend on many different factors such as light pollution, how much motion you want to capture in the explosion, etc. I like to mix it up a bit by shooting some with shorter or longer exposures to get a variety. If you do not have a shutter cable, set your camera shutter for 8-10 seconds (more or less depending on the type of shell), wait for the sound of the shell being launched and then press the shutter button.
If you are new to shooting in manual mode or have never tried, shooting fireworks is a great exercise that can show you how each setting can affect an image. It is all about learning the exposure triangle (aperture, shutter speed, & ISO). Understanding how those work are vital for any photographer.