The existing battery is glued in place. It will take a bit of prying to remove it. Be careful you don't puncture the battery.

I slowly worked a flat-blade screwdriver under the battery, prying it up a bit at a time.

Replace the old battery with the new one. I didn't bother to glue the new one in place, as it is nestled securely in a plastic cavity within the case. Plug it in to the circuit board, and reverse the disassembly steps.