Monitor cases are typically made of high impact plastic and should be dusted frequently. A cover will reduce the need for dusting. Rubbing alcohol without perfume or skin moisturizers can be used to remove fingerprints or soiling; apply to a cloth and clean the spot. Avoid using alkaline household cleaners, which can damage the plastic case. Never pour cleaning fluid onto, or direct its spray into, electronic components.
If you have an LCD monitor, don't use solvents such as alcohol, which can damage the screen. Use a soft cloth dampened with a solution of a couple of drops of liquid dish detergent mixed with water to clean LCD flat panel monitors. Then, wipe the screen thoroughly with a clean, soft cloth moistened in water to remove dirt and detergent residue. Buff dry with a third soft cloth.