Cleaning the screen

My notebook screen is dirty, but I'm afraid I'll damage it by cleaning it in a bad way. What would be the best way to do this? I have a Fujitsu-Siemens Amilo D 8830. Thanks for any answers in advance.

P.S. I bet I'm not the first one asking about cleaning a screen, but I wasn't able to find a similar topic on this forum...

Use a very soft 100% cotton cloth moistened with warm water.
If you have oily finger prints on your screen that don't wipe off with a warm damp wash cloth then you can use a very, very, very tiny amount of dish soap mixed into your warm damp wash cloth. I really mean a very small amount of soap. So small an amount that when you wring out the wash cloth no suds are made.
After wiping the screen with the very, very, very slightly soapy moist wash cloth wipe the screen with a second wash cloth that is very, very, very slightly moistened with warm water to remove any soap residue from the screen.

Never ever use a window cleaner with ammonia in it. The antiglare coating on the screen will be damaged.
For really stubborn marks you can also use isopropyl alcohol.

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Thanks for the answers!