Instructions
Disconnect the USB cable, then turn the controller so that the buttons and analog sticks are facing away from you. You'll notice five small screws on the back of the controller: one on each of the four corners and in the top-middle.
Use a crosshead screwdriver to carefully remove all five screws. Press down on the bottom of the controller (between the two analog sticks) and slowly lift up the back part of the controller.
Carefully lift the back part of the controller over the two trigger buttons on top. Be careful not to accidentally detach the trigger buttons by using force when pulling off the back cover.
Lift the battery slightly to expose the wire with which it is attached to the circuit board of the controller. Pull the battery wire (the red and black cables) from the connector on the circuit board.
Dispose of the old battery in a safe manner and attach the new battery to the exact spot on the motherboard where the old one was attached.
Slide the back cover back into place, then fasten it securely with the five screws.