You may need to provide a little more info on your camera - Sony has made over 500 models of Cybershots, with as many as 20 currently on the market. Each has quite different capabilities, and how they are used for night shots will differ based on the controls offered and shutter range available.
My basic advice would be the simple stuff to follow with any camera for a pure beginner: Go into the scene mode with an icon of the crescent moon (night mode), set ISO manually to 80, 100, or 200, set the self timer to take the pic for you, place the camera on a tripod or a flat level surface (top of a wall, garbage can, etc), half-press the shutter to get focus, then fully press the shutter and HANDS OFF the camera. Let the self timer snap, and remember the shutter may be open a few seconds so don't go to grab the camera right away.
Once you get into more advanced stuff - you can learn to set your camera on a tripod or level surface, set the lowest ISO, then use Manual mode to set the aperture and shutter speed yourself...or use shutter priority modes to set the length of shutter you want for a given situation and let the camera choose the aperture. But some cameras don't have manual controls, so that's why knowing what camera you have may make a big difference.
I love night photography and have been taking it for many years with half-a-dozen different cameras, from ultra-compact P&S models to DSLRs. They're all capable of very nice night shots - even the compacts - as long as you understand the camera's limitations and learn to get the most out of them.