Computer screens will get dirty over time from a build of general dirt in the air. Also, every time you sneeze, take care not to aim at your screen. Computer screens also show up fingerprints as well so take care not to put your fingers on the screen. Whether you have an old-school CRT or an LCD screen the way to clean it is the same. You want to wipe the screen with a soft cloth. If you need to, dampen the cloth slightly but not too much. Make sure no excess liquid leaks down the screen as this can damage its functioning if it leaks into electronics. Electronics + water = computer repair here we come.