The official word on LCD cleaning in Apple manuals is to use a solution of diluted isopropyl alcohol, no more than a 50% solution. Usually the rubbing alcohol you buy at a drugstore that is either 90% or 98% pure but 98% is pretty hard to get (you don't need it anyway). I mix 1 part water and 1 part 90% isopropyl alcohol, which works out to... um.. something just under a 50% solution.
Be absolutely sure to use a very VERY soft cloth. I use a piece of soft flannel. Do NOT use paper towels or anything more abrasive than an old worn out cotton Tshirt. Absolutely do NOT use windex or anything with ammonia in it, it can etch the screen surface and can cause the plastic to go cloudy. You don't want that to happen!
BTW, there is a commercial cleaning solution called something like Klear-Screen, it's pretty expensive. It is merely a 50% solution of isopropyl alcohol and water. Just like I make, for a fraction of the cost.
Chk in the Below link on cleaning LCD monitors
*www.klearscreen.com/