It's a holiday week here in the States, so no big lesson. Just a small one.
This is actually two images. They were combined by copying image two over image one in Photoshop. A new layer gets created. Since they were both from the same camera and precise alignment wasn't necessary, I didn't need to do anything else other than change the Blend mode to Lighten. Did some fireworks just go off in your head?
Bonus lesson: note that these fireworks aren't blown out (there are some small highlight blowout areas, which you'll never avoid), but the main elements are within proper exposure. Exposure is mostly determined by aperture, ISO, and distance to the fireworks. The closer you are, the more you probably need to stop down, especially if you're using long exposures as I was here. Don't get caught up in the fireworks display. Take an early exposure and evaluate it carefully. Note that in most programs the intensity of the fireworks will get higher, especially at the end, so if you start with overexposure, you're going to get a mess of blown values at the end.