You don't need to buy expensive cleaning solutions.
Get some rubbing alcohol (isopropyl alcohol) and make a 50/50 solution with distilled water. Then use a clean lint-free cloth, cotton flannel works well too.
Spray the cloth, not the screen, and be sure the monitor is off when cleaning it. Gently wipe it with a consistent motion.
(Using a paper towel or dirty cloth can scratch the screen, also using methyl chloride, acetone, ethyl acid, ethyl alcohol or ammonia-based cleaners can damage the screen, LCD monitors are especially sensitive to these agents.)
This is a very inexpensive method and should last quite a while.
For a good guide go
HERE,