The case comes off the front display by bending the frame around clips in the hinges. On the side with the cable, bend the outer edge toward the screen to get it around a post.

The side with the cable has an insert that tends to slide backwards when the opposite side isn't holding it in place. Push it back in during reassembly if you're finding that you can't get the case to fit back on.

To get the mechanism side off, it takes a little more bending force. Bend the left edge (hence the rest of the frame) outwards toward the screen to get it off, and it'll release around the metal hinge mechanism.