Put on Manual mode.
Turn off Flash.
Place the camera firmly on something else for a stable shot, so it won't shake
Turn on Slow shutter function, then adjust the shutter time.
You will know how to set the shutter with enough trial and error exprience. You can find this function at exposure section but you have to enable it first in the Main Menu..
To further minimize camera shake, set to 2 sec self-timer so you can completely take you hands off the it while taking picture..
The simple Canon can be a very good night shooter... lets take a look at the samples