How to set the cover photo of a “shared” Photos 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.)

First, there is no way to move the "Camera Roll" album and the "My Photostream" album. These two albums are always at the top and in that order.

To arrange any other albums, including the automatically created "Videos", and "Panoramas" just tap "Edit" in the upper right corner. You can now tap (hold) and drag these albums around as you desire. They drag and drop in the same way that your home-screen icons do. When you have adjusted them as you like, you can tap the done button.