Those smudges on your computer screen are so annoying, and they seem to keep coming back no matter what you do. Luckily, they are easy to get rid of if you know the proper procedures.
A computer monitor is an interesting piece of equipment. Have you ever pressed your finger against the monitor and seen it make those colours? It's cool looking, but it is also not good for the monitor when you do that. The oil in our skin is one of the things that makes for those ugly smudge marks on the monitor. Oils and other secretions from foods can do the same thing. None of them are good for your computer, so you should clean them off every now and then.
Using a monitor wipe is easily the best way to clean a computer screen. They are available from many retailers, they are inexpensive and incredibly easy to use. Monitor wipes come packaged like a moist towelette (the kind you get in a restaurant when you order ribs). However, they are not the same thing, and cannot be substituted for each other. Tear open the wrapping and take out the towel. Unfold it and gently rub the screen with it. You can rub just the smudges on your screen, but you should probably clean the whole thing, since your screen no doubt collects dusts every day. Rub gently. The towelette probably cannot hurt your screen at all, but rubbing the monitor really hard can't help your cause. Even though the towelette is sort of wet, it will not harm your screen.
If you don't want to buy monitor wipes, or just plain don't have any, you can also use some sort of smooth, silky cloth to do the trick. Something like a glasses wipe would be a good choice--those small cloths that sometimes come with fancy sunglasses. They are silky smooth, small and perfect for wiping out smudges. In fact, that's exactly what they do for sunglasses.
If you don't have monitor wipes or a silky-smooth cloth, just grab yourself a clean T-shirt and wipe those smudges out. This is a total poor man's solution to cleaning your monitor smudges, but rest assured, it will work. Just make sure to rub gently along the screen, being careful not to push down against the monitor too much when cleaning. You should have your smudges out in no time.
Whenever you clean your monitor, you are just wiping the surface. So don't push down hard on the screen. This will only bruise your monitor in the long run.
Never clean a monitor with anything wet unless it is specifically designed as a monitor cleaner. Those moist-towelette monitor wipes are fine, but don't ever use water.