A video from this thread..
First you clean it with a dry microfiber towel. Then use a Magic Eraser, which gets rid of the filmy buildup. Finally, use a streak-free glass cleaner (he uses Zep) to get it completely clean. IME it really works, especially for the film.
In terms of getting to the corners & tight spots, grab a nearby 10 year old with small hands to clean the edges for you.