Avoid using windex! it has corrosive properties that can damage a flatpanel display!
Instead try to find a 50% solution of rubbing alcohol, this works best. In fact, a lot of the products marketed as screen cleaners are just this. If you can't find a 50% solution, then the 70% solution you find in drug stores will work alright too. If you can, dilute it with some distilled or deionized water; don't use tap or mineral water as they can leave residues.
Try to use a microfibre cloth, or something cotton. Paper towels, or even regular towels, are slightly abrasive and may leave microfine scratches in the screen. Do not spray the solution directly onto the screen. Instead spray some on the cloth and then begin wiping. For best results, turn the monitor off or to something very dark when you're cleaning; it's much easier to see streaks and such this way. Lastly, make sure you don't leave any wet spots and wipe thoroughly.