Learn how to wipe away those smudges with ease and how to avoid doing things your computer screen would not appreciate.
Choose a microfiber cloth. This is ideal for cleaning a computer screen.
Turn off the computer before commencing to clean it. It is usually much easier to see where to clean when the screen is switched off.
Give the screen a once over by brushing it with the microfiber in small circles.This will remove the majority of simple imperfections.
Only if truly needed, moisten a cotton cloth, even the corner of your cotton shirt, and repeat the small circular motions. It may actually be enough to just breathe over the screen and use that moisture to clean with.
Read the instructions accompanying the cloth you're using. Some of them need to be made slightly damp before use. If this is the case, skip this step and follow the cloth's instructions instead.
If dampening a cloth, it is best to use distilled water.
Brush again with the microfiber cloth to finish off. Don't over-rub though! And if there is any dampness left, just leave it to air dry.
Do not put too much pressure on the screen when cleaning it.