I have to add that not only does Larry's answer work, it applies to the Olympus Stylus 500 as well. Open the battery door and use a very tiny Philips screwdriver to remove the black pad attached to the inside of the battery door. There are two miniscule black screws that must be removed. Be sure to remove them over a light-colored counter so as not to lose them.
When this is done, close the battery door, and then use a tiny flathead screwdriver to lift the back of the battery door up as you push back on it as if you were closing the door as usual. Do this gently and the door will slide backwards over the bottom of the Stylus 500 case. Pop it the rest of the way off and then replace it with the new battery door in the same basic fashion Larry describes with the 820. The only difference is that the black insert still needs to be replaced afterward.