I dont know which type you have but here is how to clean either:
Those big chunky CRT monitors
have glass screen which are easily cleaned. The important thing to remember is that you don’t ever want to spray any liquid directly on the screen. Instead, spray the cloth with water or a mild window cleaning solution then wipe the screen. You can use the same damp cloth to clean the entire monitor case, as well. If you prefer, you can also use moistened paper towels to clean CRT monitors, You will be only cleaning the outside of the monitor case and screen. Never open the monitor casing which contain electric voltage that can cause a shock.
Flat Panel LCDs
LCD monitors are often called flat panel monitors
because they are flat and thin. These are the types of screens that are used in most laptop computers
, and they are also becoming very popular for desktop computers. LCD screens are softer than CRT glass screens, so they require some extra tender loving care. Keep your fingers and sharp objects away from these screens since they are susceptible to damage and scratches.
Use a soft dry cotton cloth to remove fingerprints and smudges from the screen. If this does not completely remove the dirt and splotches, use a small amount of isopropyl alcohol on the cleaning cloth that has been dampened with water. (A small amount of vinegar can be substituted for the isopropyl alcohol.) Again, spray the liquid on the cloth and never directly onto the screen. Do not use paper towels on an LCD screen as they can scratch the screen. Never use ammonia, ammonia-based cleaners, or strong cleaners which can cause the surface to yellow and become brittle.
It is good to have a special clean cloth that is dedicated to use on the LCD screen. Don’t pick up any old rag, as dirt particles in the rag can scratch the surface of the screen. Special LCD cleaning cloths are available and can be an excellent investment