The single best photo accessory one can buy is a tripod, and it is the biggest key to good fireworks photos. Beyond that, I'm going to disagree with some of what has been said here, but it all assumes tripod use. It should go without saying that you want to be unobtrusive to others in where you set up.
First, use the lowest ISO setting. The higher the number, the less sharp the image. Fireworks are bright, high ISO speeds aren't needed.
Next, your shutter speeds should be
seconds, not split seconds.
The aperture should be around F8 for low ISO speeds, F11 for 200, or stop down to F16 for 400. These are starting guidelines. If they are looking too dark, open the aperture; too light-stop down.
Since most digital cameras have a monitor on them, you'll be able to quickly see if a setting needs to be changed, so that's a plus. If for some reason, there's no monitor on this camera, or for anyone using film, you should bracket your photos. For instance, if the probable shutter speed is 5 seconds, do other photos at 3 seconds, as well as 8 seconds.
These settings are all connected. For instance, if you're at ISO 100, F11 and 1 second, and want the photo brighter, you can change the ISO to 200, OR open to F8, OR go to 2 seconds. Any of these moves will be increasing the exposure by 1 stop.
I've never used the covering the lens trick between bursts, although I'm aware of it. That will work best if you just getting the FWs. But you may want something in the foreground as well, such as the castle.
http://home.comcast.net/~ralfrick/disneyland_14_.htm
(Low res image originally shot on film)
Therefore, I would determine the best exposure for the castle at night with a low ISO speed set at F8; it will probably be about 5 seconds. Once you know that exposure, assuming the brightness of the castle lighting is similar, that should be your starting point for pics with the FWs.
Since there are videos of the shows on the web, seek one out to get a feel for which specific points of the show would make the best still photos. A lot of this is intuitive by nature. You can take a photo, see in the monitor that it's too bright, but, of course, the next one will be different anyway because the fireworks themselves will be different. Lot's of them won't work out too well, but don't worry about it; it's not like you're paying for film.
I'm giving this advice based on the "
National Geographic Phtographer's Field Guide", which is currently in front of me, and my experience, which includes a BFA in photography. Good luck and have fun.
Cheers