Welcome to Tom's Hardware Forums,
The other side panel should come off like the first - it just doesn't have a grasping point at the back. Unscrew the two screws at the back holding it on, slide it toward the rear. If it does not come off easily that way, it may not have to - the video linked below shows an Acer tower optical drive replacement where only the one side is removed.
To swap out your optical drive, you will need to remove the front panel also. Some front panels have clips you'll need to release from the inside while some have posts and simply pull off toward the front (usually from the bottom), some have a combination of both. This video may be helpful http://www.youtube.com/watch?v=LbF14QT3Fks
Hope it helps