Based on products sold in stores specifically for cleaning LCD displays, here is what I suggest:
- Mix equal parts rubbing alcohol and water in a clean spray bottle (no windex, etc. left in bottle).
- Acquire a lint-free cloth made for cleaning eyeglasses and displays.
- Spray, wipe, repeat (if necessary).
It has been suggested that eyeglasses cleaner works as well, however I have have not tested this.
DO NOT USE WINDEX ON YOUR SCREEN!