How to take night shots with digital camera?

How to use the night mode? How to determine shutter speed at night?

Well, most mordern cameras will determine the shutter speed for you in auto/program/aperture priority mode. Your bigger worry would be how to hold the camera steady for the required length of time which in the case of night shots can easily range into the seconds.
In this case, a tripod would be your best bet. Mount your camera on the tripod and set to one of the modes above. If you have your own exposure meter, you can also set your camera to manual and set the shutter/aperture values yourself.
Use the timer or remote control if available to snap the picture since physically pressing the shutter button may shake the camera and cause the picture to be blurred.

try with your manual

if its a digital camera than it adjusts on its on, even when you see darkness on the screen, it clicks the picture ever so clear.
There is nothing like night mode in digi cam.