I'd start by opening the cart with a small gamebit driver. It's the same one that opens all Nintendo carts.
The battery should be obvious. I don't know if its specs will be marked clearly, though. A trip to Radio Shack will probably ID it though.
I don't know how to remove the battery from the board, but I wouldn't use much force. You may have to solder on a new battery.
http://www.retro-games.co.uk/museum/repairs.htm has some details on SNES battery replacement.





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