This guide worked really well for me! I got the ifixit adhesive remover, which worked well to clean off the old adhesive on the back cover and beneath the battery. I also got the 4mm roll of Tesa tape, which was about the same thickness as the old adhesive, and made it easy to cut strips of appropriate size to replace all the spots where the old tape was. I have plenty of tape and adhesive remover left over for future repairs.
After putting in the new battery and connecting the small “press connector” at the end of the cable ribbon, I would recommend plugging in your phone to make sure the battery is charging before replacing the back. If I could do this all over again, I would go ahead and replace the fingerprint sensor while I had the phone open, they’re notorious for failing on the G6.