Nighttime shots are going to be hard to do really well without some fancy equipment.
That being said, the following will all promote higher quality night pics.
1. A tripod - camera shake is your enemy. It's all but impossible to hold a camera steady for long exposure times.
2. Basic camera settings - As others have posted already, you need to understand the pros and cons of the 3 main settings of your camera. Changing one up or down directly effects the other two.
3. Shoot a ton of shots, even at settings you think won't work. You will be amazed what post production can do. Especially underexposed shots. Since you are shooting dark things with random bursts of light source, underexposing tends to yield the best results.
In general I use the following settings as a starting point, and then tweak as needed.
ISO - 400 or less (I get too much noise above 400)
Aperture - 2.8
Shutter Speed - Whatever the camera tells me I need to use in order to get a neutral exposure.
From there I adjust everything up and down a couple of clicks and shoot a few more times, again focusing on underexposing most of the time.