Each computer model is slightly different. You can determine the behavior for your particular computer by selecting Start, Shutdown and the selecting Sleep. You should see a change in the power light on the front panel of the computer. The power light may change color or simply flash.
Keep in mind that your monitor is separate from your computer. Unless your computer is an "all-in-one" where monitor and computer are merged into one stand up unit, your monitor will usually go into sleep mode prior to you computer going into sleep mode. The power button for the monitor will also change color or flash when in sleep mode.