As most things you can shoot with what u got. Whether it's a point and shoot with a firework mode or a top of the line DSLR with some sexy glass, anything will work the only necessity is a tripod, you have to keep the camera super still throughout the duration of the firework to capture the full light trail with no shake so your images are super sharp. There are things we all want that will make our shots easier to capture, the one fairly inexpensive thing is a cable release, this is one of the few occasions this come out for the simple reason I can use bulb with out touching the camera.
The settings for the fireworks is the one thing that when I started I thought there was some kind of magic setting, but when u learn how the camera works it couldn't be simpler. If you are using a point and shoot make sure the flash is off and go to night mode or, put it in to firework, how easy is that. Using a DSLR I start with f16 ISO 100 and shutter into bulb, attach the cable release when the firework starts to go up push the button and when it has finished let go simples, now this is not written in stone if you take a shot, review it then use your knowledge of exposure to get it correct for the situation your in. If you are not using a cable release set the shutter speed to about 2 seconds take a shot and then review, if you are not capturing the hole explosion you want to make the exposure longer 3 maybe 4 seconds, review then set ISO and aperture according.
For the focusing the way I do it is set it to infinity ( yes on some things I do take the incredibly easy way ). The better way to do it is wait till one of the bright lights shoots into the sky quickly focus on it then switch it to manual focus then leave it there and shoot away.
Hopefully this gets you on your way to shoot on this one day a year unless you get some for new year I suppose. I will be posting some more after the next time I shoot fireworks a part 2 if you will.