If you're replacing the battery on the left earbud then the pad corresponding to black wire will be labeled BAT - on the PCB. (Photo 2)

If you're replacing the battery on the right earbud then the pad corresponding to red wire will be labeled BAT + on the PCB. (Photo 3)

Heat up the solder on the pad and insert the wire into the melted solder.

Holding the body of the battery in between two fingers, you can more easily manuever the wire into the melted solder

Repeat the above steps for the second battery terminal wire

Using tweezers may be useful in manuevering the second wire into place

Make sure that there is no solder that is bridging the two pads together that would short circuit the battery.