I've been pretty careful with my MacBook laptop screen over the last year and a half, but nonetheless it had accumulated some fingerprints and various reflective spots. These would not be noticeable most of the time, but with the illumination in the correct place they showed up quite strongly.

I've searched for things like "how to clean macbook screen" but with mixed results. The problem is that there are (at least) two different types of MacBook screens - matte and glossy finish. Mine is a glossy finish. Since LCD screens are often sensitive to what liquids you put on them, I wanted to avoid damaging my screen.

Finally I found something (I don't recall where) that said plain water with a soft cloth is all that is needed. So using a clean microfiber towel (from REI), I wetted a corner of it and carefully wiped the screen. I had to pay particular attention to areas that were affected by fingerprints and whatnot, but all the marks came off nicely. With a dry part of the towel, I dried the screen so no remaining water droplets were left.

The result is an absolutely clean screen that looks great!