It depends on the type of monitor.
If it has a matte layer (antiglare), get a microfiber cloth. Moisten the cloth and wipe down the screen. Dry it with another (dry) cloth.
If it's a touch screen, just wipe it down. Liquids can cause "false touches" and cause issues. If it's really bad, use a tiny bit of water on a microfiber cloth, or turn the device off (really off, not locked) before following the directions below for clear glass.
If it's just regular clear glass, use baby wipes or Windex with a microfiber cloth.
Never ever EVER use paper products! Due to their extremely rough surface, they cause scratches in the screen. They might not be too obvious, but they build up fast.