Taking great underwater photographs at night can sometimes be done using just your camera, while keeping your flash on. They may be a little grainy though, and without a light source, you won't be able to see anything anyway. Using a light source ensures that your photos come out just as well at night, as they would during the day. It also helps in other obvious ways, such as allowing you to see where you are swimming.
You can buy strobe light attachment's to use as a light source, but underwater strobe lights could seriously cost a small fortune.
I personally use a StealthLite 2450, Rechargeable Xenon Dive Light. This small flashlight can go down to depths of up to 500 feet, and the light that it gives off is plentiful. The best thing about the light though is that it only costs $60.00, is rechargeable, and will provide a perfect amount of light for you to focus in on your subject. Basically the inexpensive light allows you to snap a marvelous photograph.