1) Fireworks displays can be a wonderful opportunity to create powerful photographs. My goal is to break away from the traditional imagery and capture something totally unique. To get started you just need three essential pieces of gear. My typical setup for photographing fireworks is a tripod and ballhead, a DSLR camera, and a telephoto zoom lens. While I shoot with a focal length of 70-200mm, just about any medium telephoto lens will do. You'll be doing a lot of shooting, so a full battery and empty memory card are also recommended.
2) In order to experiment with different effects, you will need a slow shutter speed. My exposures typically fall into a range of 1 or 2 seconds. With the shutter open for a longer period of time, it gives me an opportunity to manipulate the lens, move the camera, and manually adjust focus. You still need to work quickly, but this is where the tripod helps. With the camera supported, you have your hands free to make adjustments.
3) Using a medium telephoto zoom lens is my chosen method as it allows you to actually zoom in and out during the exposure. This can yield some otherworldly effects and streaks of light. I sometimes start recording photos at 200mm, then twist the lens back to 70mm. Some captures start at 70mm, and end at 150mm or longer. Since this is not a method we normally use in photography, it can seem a bit awkward at first, and may require some practice to make it a smooth motion.
4) Since it's typically quite dark during fireworks displays, I always focus manually. While autofocus on today's most sophisticated DSLRs could actually work, I find that manual focus provides more creative control.
5) Besides zooming in and out, you can also adjust the focus so an exposure starts in sharp focus, and is then twisted out of focus. The result is a soft glow of color around sharper details. Again, there is no right or wrong method here. Success ratios are the last thing on my mind, as the goal is to create something totally out of this world.
6) Although my camera is on a tripod, I try to purposely move it during the exposure. To do this, simply pick it up and walk a few inches in any direction. While unconventional, the results can be quite interesting.
7) The landscape painter Bob Ross used to say "We don't make mistakes, just happy accidents". The same is true with this kind of photography. This is a terrific opportunity to work outside of the guidelines and let your creativity flow. The more rules you break during this process, the better. Best of all, you can do this from your own backyard. Have fun, be safe, and enjoy!