Don't buy any cleaners as they more than likely will leave a permanent white-ish streak on the surface of the LCD screen. I've seen it happen too many times.
use what user00000 said...cheap and works well!
I am a rental computer technician for a living and I have discovered that using 50 percent rubbing alcohol and a microfiber cloth works wonders. Too strong of alcohol and you start messing up the finish.
I take a lintless rag, dip one end in water, wring it out, and slightly moisten the screen, then take the dry side and buff it out. Got to do it quickly before the water begins to dry or you'll get streaks. Do this while the computer is completely turned off and the battery is disconnected.
I have absolutely no experience regarding the topic, have done no research and do not have the faintest clue as to the ins-and-outs of cleaning your screen. But, since when did I allow a total lack of knowledge prevent me from expressing an opinion?
Take the thing down to the do-it-yerself shove-the-quarters-in car wash with the power spray.
Use said power sprayer.
If a "foaming brush" is an option.... utilize the device.
Don't recomend the wax option.
Another option is eyeglass lens cleaner, which I conveniently have several bottles of. Turned laptop off, removed power cord, carefully tilted laptop so screen was flat against the carpeted floor (I was supporting the rest of the laptop with my leg), spritz screen with eyeglass cleaner, wipe with clean microfiber cloth, flip cloth over and buff till dry. No streaks!