Whether one is shooting fireworks or stars or anything else in low light with some discrete bright objects, there are a few critical concepts:
1. A steady camera is a must: tripod and release cable will work well and in critical situations you can even use shutter delay to reduce camera motion caused by the shutter movement
2. Exposure for the bright objects
3. Use shutter speed to capture difficult to time bright events
So the first two examples are just old fashion firework pictures. These were taken at ISO 100, f9 (and perhaps I should have pushed that up to f11 or so), 24mm and a manual (bulb) shutter release controlled with a release cable. Camera focus was focused on an object at about 7-8 feet and then switched to manual. I selected this distance by calculating the hyperfocal distance for my lens/camera. A nice piece of software for this calculation is called DOFMaster.
If you want to see more examples, please visit this page of my website.
For the next picture, I used ISO 100, f9, 58mm for a total of 30 seconds. I adjusted the expoure duration and aperture so I can leave the shutter open long enough to capture the random and untimed firing of fireworks across the lake. In this way, I did not need to time the firework which are quite bright when they are fired.
And for the last picture of a meteor, I first decided my exposure time maximum. I determined this by dividing 600 by the focal length (24mm) or 25 seconds. I then selected the aperture and ISO to yield a nice exposure of the stars. In this case it was f2.8 at ISO 1000 and this exposure value did not blow out the lights on the ground too much. I also focused my camera on the horizon and then switched it to manual so it would not change. Once my exposure was set and my camera was placed on a steady tripod, I then turned on the interval shooting timer (in Shooting Menu on the Nikon D800). I discovered the interval timer needed to be set longer than the exposure time. I selected 28 second intervals so I lost about 4 seconds of exposure and to capture this one image I took 400 images for a total captured time of about 3 hours. This is the single picture I got of a meteor during the Camelopardalids meteor shower.