Hi nochus. I'm not sure what you mean by "go off automatically". If you mean the monitor doesn't power down when the computer switches off, then this is a function of the monitor. Most modern monitors will go into a low power standby mode in the absence of a signal, so you need to refer to your monitor manual, which may be on a cd that was supplied with the monitor.
If you want your monitor to go into standby after a period of no computer activity, then this is a "Power Management" function. Start - Settings - Control Panel - Power Management. Under the "Power Schemes" tab, scroll down to the "Turn off monitor" time you want, and click OK.