You'll have to start by telling us what kind of monitor it is (arcade, PC, etc.), and what you want to mount it to (upright or cocktail cabinet).
I'll make the assumption you are talking about a PC monitor in an upright cabinet. In that case, the easiest thing is to build a shelf in the cabinet and place the monitor on the shelf. You can paint the case of the monitor black in the front and use tinted glass to cover the front of the monitor.