The glass front of your monitor could just be wiped over with a bit of window cleaner and an old rag. You could give it a bit of elbow grease if there where any persistent finger prints, and in a couple of minutes it was as good as new.
But what is the best way to clean a LCD/TFT type of screen? They are not made from glass, but plastic, and it is very fussy plastic at that. Window cleaner would probably be a bad idea since it has things in it that can eat plastic. Instead, I often use a little cotton wool which has been very slightly dampened with a drop of pure water.
Cotton wool is better than using a rag because not only is ultra clean, but it is the least abrasive substance I know of. Soft tissue paper might seem like a good idea, but I tried that and it left lots of little fibers behind. Dampening the wool shouldn’t be overdone because you don’t want water getting on your screen.