they say those microfiber cloths are the "recommended" way to clean any display, but for extra dirty screens, all your going to do is smear the oils around on it.
Windex is fine, as it's alcohol based and made for cleaning glass and plastic screens.
Apply about half a spray to soft cloth or very soft paper towel.
Wipe screen with cloth and make sure the screen is fully dry after making it clean.
Never use a dirty cloth, otherwise it'll streak and add crap to the screen.