I use one of those micro-fiber cloths, seems to work quite well, and doesn't scratch the screen. Use the cloths to clean my glasses too, which are plastic lenses and have had no issues. I keep a couple of them in the console, they’re cheap and readily available.
Yup, I use them dry. I also have similar for my windshield, reaching the whole thing and especially getting into the inside corners was difficult, so I bought a window wand with a triangular head on it, covered by the same type of micro-fiber cloth, works great!
As with any LCD or plasma display screen, do not use anything with alcohol or strong detergents. The chemicals in those can destroy any anti-glare or other type coatings on the glass. And do not use any abrasive cloth as that can scratch the coating and glass. It is best to use a dry micro fiber cloth and a small amount of distilled water only if a dry cloth will not clean the screen. There are some products in stores that sell televisions for cleaning the screens, but I have never tried or trusted any of those.