O-ring replacement has 2 steps.
First you want to unscrew the back of the figure in question. Most hobby stores and hardware stores sell varieties of Phillips head screwdriver types. You will want a small philips head. Maybe even bring a figure with you to the store and use it to find one that is a perfect fit. Too big and it wont be able to get to the screw, too small and you have a bigger chance of stripping the screw. Just like the porridge in Goldilocks, you want one thats “just right.”
Sometimes you encounter a rusted or stripped screw. If the screw is simply rusted, I have heard that applying Coca-Cola to the screw and leaving it for a few days actually helps this. I have never tried that. Also, a quick shot of WD-40 sometimes works. If the screw is too rusted or stripped, you have to remove the head of it with a dremel drill. If you don’t have one, chances are someone you know does. Also, almost every hardware store sells them (They are a great tool to just have for any project!)
Find a drill tip again that is small enough to fit in the hole in the back. Use the drill and literally drill the top of the screw off. I can’t tell you that this wont damage the figure, but if you do it carefully, it should leave little to no damage.
Once the head is drilled off, you should be able to pull the figure apart.
Step 2: O-ring replacement
Remove the broken or rotting O-ring. Usually in the plumbing section of hardware stores, they sell varieties of )-rings. GI Joe figures typically use either a #8,9, or 10 size O-ring. They are very cheap (usually around 30 cents) so see which size fits your needs best. Some online Joe retailers sell bags of O-rings as well.
Once the New O-ring is in place, reassemble the figure and screw the front and back together again. If you have destroyed the screw you can sometimes find new ones at hobby shops, some hardware stores, some online stores, or you can cannibalize a “beater” joe you have laying around.
O-rings are notorious for just giving out at odd times. I have come home more than once to find my Destro figure in 3 pieces!