The fireworks picture below was taken with a technique involving holding a black card in front of an open shutter. In manual exposure mode, set the shutter speed to 20-30 seconds (or use bulb mode), an aperture of F11 to F16 and an ISO setting of 100 or 200. Using the bulb mode on your DSLR, you can get the shutter to stay open as long as required. If you are using the bulb mode, a remote shutter release is very useful to avoid getting camera shake (yes it can happen even on a sturdy tripod).
Timing is Crucial
The single most important tip I can give you regarding night photography is to get a good tripod. With a sturdy tripod, you can use the most basic camera and lens and come out with a winning shot. Armed with a tripod, the next thing to do is to scout for a good location where you can set up your tripod and wait for the twilight hour when the amount of ambient light matches the amount of artificial light. This creates pictures where the sky is a deep blue color, perfect for offsetting the man-made lights in the scene. If you are shooting a low ISO setting like 100 at this time, and your aperture in the F11-F16 range, your shutter speed will drop to a level where it is not possible to hold your camera steady. That is why you need a tripod.
Shooting Light Trails
Use a small aperture (which means a big F-number like F16) to get starburst effects on street lamps like in the picture below, taken in Ubud, Bali. Not only does a small aperture give you more depth-of-field (which means objects are sharp from front to back), it also enables you to get longer shutter speeds, which contribute to the long red lines created by the tail-lights of passing motorists. Or white lines created by their headlights. The easiest mode to shoot this is Aperture Priority.