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!