Special care must be taken when handling an LCD screen
, especially when touching or cleaning it. First and foremost ... avoid touching the screen. No really, don't touch the screen. Ever!
Evidentially I haven't repeated that enough in my house. Right now, I'm looking through the glare of a number of tiny fingerprints (again.)
Apple's website, recommends cleaning LCD's by turning off the computer (or display) and wiping the screen with a damp, clean, soft, lint-free cloth. Paper with water only. This works ... but only if you've never touched your screen. Basically this method gets the dust off, and that's about it.
For getting fingerprints (or worse) off, try a simple 50/50 mixture of 70% isopropyl alcohol (Apple does not
recommend this) and distilled water. Mix the liquids in an empty spray bottle. Next, turn off your screen, dampen a microfiber cloth with your 50/50 mixture and begin wiping the display–gently–from top to bottom. This should do the trick.