I've always had good luck with a damp (not WET) paper towel. It gets most stuff off, just make sure it's not wet enough to drip and roll down to the edges of the screen. Then just dry it off with another soft paper towel or tissue or cloth. And remember not to press very hard on your screen. If there's still some stuff on there you can't get off, you might try adding just a tiny bit of soap to the towel, and that should do the trick. It's cheap and effective -- good enough in my book!
I have one of these cloths that I use for the lens and screen of my digital camera. It's a dry process, just lightly wipe it across the lens/screen, and it's absolutely incredible how well it works. These cloths are also available at any major photo shop, like Ritz Camera. These cloths are probably microfiber material, which means you could do just as well going down to the auto parts store and buying a microfiber detailing cloth like the one Meguiar's offers (Ultimate Wipe ):
I use glass cleaner, clean in small areas. Use a light to find out which areas you've missed. If you've never cleaned it before take your time it'll take awhile. Use a paper towel, napkin, don't use something that gives off lint otherwise you'll have a clean screen with white specs all over. Spray the towel, not the screen. Some cleaning fluids will cause white spotting on cheap plastics. Use a wet q-tip to get into the corners.