Shutter Release: I use the Nikon ML-L3 remote that syncs with my camera, it's a cheap piece of equipment that makes life so much easier. There are all sorts of cable release systems on the market, do some research and choose what works best for you. The release allows you to keep your hands away from the camera and avoid added camera shake. If you are just starting out and don't want to purchase a release, you can set the self timer on your camera, which will give your hands time to get away.
Flashlight: Just a regular flashlight, simply for the ease of being able to see what you are doing. I prefer to use a headlamp so that I can still use both of my hands. Another reason to have a flashlight is because usually at night your subject will be under lit, and it's helpful to be able to shine a light and achieve sharp focus.
This is really all you need to start out, but depending on your theme you may need speedlights or studio lighting, as well as many other things, but this is a basic tutorial...
Now for the setup, deciding how to get your shot. At night you need to realize that while it may be dark, you still have to focus on all the same concepts as day photography. Composition, aperture, shutter speed, ISO and white balance.
Composition: You have to think about the surroundings, if you're going for a pitch black background, it probably isn't a good idea to put your subject against a wall. Anything that will bounce light has the potential to change the shot. Keep that in mind.
Aperture: Most of my shots are a few minutes and involve bright lights, so I have to make sure to go for a small aperture in order to get the exposure correct. And as always, use the aperture to control your depth-of-field. Remember, large aperture=shallow depth. I also need to mention that with a small aperture, (f/16 and smaller) you will see a starburst around the lights in the picture.
Shutter speed: This is where the night shoots get fun, do you want to show movement or freeze time? I usually prefer motion, so I use longer shutter speeds. The trick here is to figure out how long it needs to be open. If you're photographing a snowboarder in motion, it doesn't need to be very long, and realistically shouldn't. ( the longer it's open the longer the subject has to perform) but if you're wanting to show movement in the stars it needs be longer than ninety seconds.