What I use to clean desktop and laptop LCD screens (as well as other parts), is vinegar. What I do is take a clean lint-free cloth, damping it with some vinegar, wipe down the monitor, then quickly dry it with a lint-free cloth. Vinegar is a natural substance, so it doesnt have harmful chemicals in it, such as glass cleaner which has ammonia.
Also when your cleaning it, make sure the screen is off and it isnt in direct sunlight, otherwise the vinegar will dry before it gets a chance to be wiped away.
You also could use specially designed LCD cleaners, however I still prefer vinegar since it's something most people have around the house, and is also alot cheaper.