Do not use any form of tissue paper or paper towel, these are abrasive and will cause micro scratches on the screen, use cotton cloth, an old T shirt is what an optician once recommended, dampened with water.

I tell Maria to do it.

Answer of the day! Except in my case it's Linda

You're from Norway so that would be Ragnhild or Gunhild. ;-)

alcohol and dina 4 paper :)

And most importantly what ever you use to clean it do it on a COLD screen not after it has been on for a while. This will stop the streaks and smudges caused by the crap drying on the screen from the warmth of the monitor as you try to wipe it off. Me i just use a water dampened cloth. Remember COLD screen

I just use that stuff you clean your glasses with, works good.

My monitor luckily included a cloth that feels very much like the cloth used to clean glasses.
I wipe the screen in straight lines as much as I'm able. (Ironically I gave my screen a clean just this morning.)

I use sawdust and a shovel.. Works every time ;)

Lol ! your all doing it wrong. Use as soft a cloth as possible and mix warm water with a little vinegar whilst the monitor is hot. ! VINEEEEEEGAAAAAAARRRRRR !