Grab you DSLR camera and a tripod. Set your ISO setting to manual and as low a setting as it goes. that means 50, 100 or 200 depending on your camera. Move your focus switch from auto to manual so the focus doesn’t “hunt” when aiming at the sky. Focus your lens on infinity. You can verify this by looking at any distant light or other object and leaving it there. Just make sure it’s an object far away.
Now that your focus is set, set your exposure (the F-stop and the speed) to manual. Most DSLR cameras offer you choices of: P, A, S, M. Some say P, Av, Sv, etc. It’s ok if your camera doesn’t show those exact choices just as long as you know that what you want is M for Manual. (You don’t wan’t P for program mode.) Set your f-stop to f8 or f11. Last setting is the speed. You can set your speed at 3 to 5 seconds. That’s not 1/3 to 1/5 but rather 3 to 5 seconds. If you have a cable release to trigger the camera taking the shot use it. This cuts down on vibration and makes sharper pictures. If you don’t have a cable release then just push the shutter button carefully to take the picture without shaking the camera. The best setting for exposure is called “BULB”. The name “BULB” goes back to the olden days. If your camera has a shutter speed setting called BULB, use it for fireworks. BULB is a setting that keeps your camera’s lens open for as long as you push the button down to take the shot (or with your remote trigger). This is what I use. I watch the rocket begin to shoot up from the ground and I press down on the remote and hold it there. Or you would just press the “take the picture” button on your camera. In “Bulb” setting, the lens will stay open for as long as I press down on the button. It isn’t a set time like 3 seconds. I keep the lens open to take the trail of the rocket going up and after it explodes and those nice streamers trail off and fade I let go of the button and the shutter closes.
The last thing to do is to look at your shot to see if it’s over-exposed, If it is, close the f-stop down (make it smaller) to f11 (if you were on f8). Or keep the lens open for a shorter amount of time.
If your lens has what’s called a VR or IS setting (Vibration Reduction setting) turn that off before your begin. When on a tripod, a lens with VR will actually take a blurrier shot unless you turn it off.