How To Shoot Fireworks » Photography Bay – Article is written by Chris Gampat, short, useful, and to the point:
Shooting around 4-10 seconds long with F11-22 should deliver the quality that you want. Obviously, you’re not using a flash as your flash will do nothing to help your images from that range. To get the cleanest image quality without banding or grain, you may want to go for ISO 100-400. Additionally, use the method of focusing that video professionals use: zoom in, focus perfectly on the subject and then zoom out to compose your shot.