It's really simple. I found this video and it's decent for a beginner. I work with circuit boards all day long at work so I'll add a few details.
1. The bit he is using is a 3.88 mm security bit.
2. I would desolder the prongs lose from the back of the board first before removing them from the CR2032.
3. Make sure you note the polarity of the battery when replacing it.
4. Solder the prongs back on the battery then back on the board. Electrical tape is for losers.
5. You can buy single packs of CR2032s at WalMart.
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YouTube - How to Change The Batteries In Your SNES Carts