Apple - How to change the cover photo of an album?

In my experience, the cover photo is simply the first photo in the album. When you're within an album, hit the button in the upper-right corner to manipulate the photos; then tap and hold a photo until it "inflates," at which point you can drag it to move it around. You'll just have to be happy with your album cover being the first photo in the album.

(Edited to clarify the tap-and-hold gesture.)

Hold down the photo you want to be the cover, copy, then paste over the top of the first photo in the album to make it your cover.