How to photograph fireworks?

Which Camera?
You need a camera on which you can manually set focus, shutter speed and aperture. The reason that you need to be able to manually set the camera is that autoexposure probably won't work, plus you need an exposure of several seconds in order to record long exposures. You also need to be able to set the focus since there may be nothing in the frame when you open the shutter so AF will fail.

Which Lens?
Which lens you need depends on how close you are to the show, mostly I used a 24-105 zoom on my EOS 400D/50D. Set focus to manual and focus at the distance at which the fireworks will be from you. If you zoom, make sure that your lens keeps focus when it zooms, otherwise you may have to refocus after zooming.

Camera settings
Well a good place to start is with a 2s exposure at f/8 with the camera set to ISO 100. The shutter has to stay open this long to record the trails of the various components of each burst. You can also try exposures of 4s and 8s if you want less or more bursts captured. The brightness of the trails depends on the aperture and ISO setting, not on the length of the exposure. For very bright firework bursts, stopping down to f/11 might give better results. With such long shutter speeds the use of a tripod is essential and the use of some type of remote shutter release (wired or wireless) is highly recommended.

When to shoot
The problem of course is that you don't know ahead of time how bright each burst will be, when it's coming or exactly where in the sky it will be, so there's an element of luck in capturing the image. If you wait until you see the burst, it will be over by the time you take the shot, so you have to anticipate. Sometimes you can see the rocket trail going up and that can give you a clue when to open the shutter. Ideally you want to open the shutter just before the major display occurs.

Summary

• Use a tripod. You can't handhold the camera for a time exposure, even if you're using an IS lens.
• Use ISO 100. Fireworks are bright and the lower the ISO setting, the lower the image noise.
• Unless you are a really long way from the fireworks, a wide to short-tele lens should be fine.
• Stop down to around f/8. This will give you the sharpest images and allow a long exposure.
• Prefocus the lens and switch to manual focus.
• Try shutter speeds from 2s to 8s. The longer the exposure, the longer the trails will be.
• Open the shutter while the firework is on it's way up, not when the shell explodes.
• A remote release will be useful. Use one if you have one.
• Shoot lots of images. Some will work, some won't. It's a matter of luck. The more you shoot, the luckier you may get!