I found a nice trick this week. If those microfiber cloths that came with your LCD monitors and TV(s) have all wandered off, you can use a dry eraser instead. They’re bigger, so they’re easier to keep track of, and easier to use too. Just wipe the screen with the eraser like you would if you were erasing a whiteboard.
If you have fingerprints or other gunk on the screen that a microfiber cloth or dry eraser can’t remove, dilute some white vinegar 1:1 with distilled water and apply it to a soft cloth to clean the screen.