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Remove screws from the back of the controller. Remove the back. Remove the battery. Remove the screw on the motherboard. Remove the motherboard. Place the plastic stick back on the metal rod. Replace the motherboard. Screw the motherboard back in place. Replace the battery. Replace the controller back. Replace the screws on the controller back.
There are five screws holding the controller together. There are two on the top and bottom of both sides, and one on the top middle. You may need to pry open the controller with a flat head screwdriver. Open it from the bottom and carefully tilt it towards the top shoulder buttons. Be very careful that you don't accidentally dislodge the R2 or L2 trigger buttons while removing the back. They can be pain to put back on. The battery is the large grey square on the back of the motherboard. You don't need to disconnect the battery. You can just pull it up out of it's holder and move it to the side. If you do decide to disconnect the battery, pull on the white plastic part connected to the circuit board. Don't pull on the wires. The motherboard screw is located on the bottom of the motherboard next to the analogue stick. Carefully pull the motherboard up and tilt it away from the shoulder buttons. Once again, be careful not to accidentally dislodge the R2 and L2 trigger buttons. There is a D-shaped metal rod that sticks up out of the motherboard. Place the plastic analogue stick back on the metal rod. Carefully place the motherboard back in it's place with the analogue sticks freely able to move through the holes. Using the same screw you took out of the motherboard, screw it back in at the bottom next to the right analogue stick. The motherboard has a plastic holder on it's back that holds the battery in place. Place the battery back in the holder. To replace the controller back, place the the thin part that goes in between the two shoulder buttons at the top of the controller in place. Carefully tilt the back over the R2 and L2 trigger buttons and firmly push it back in place at the bottom of the controller. Be very careful not to dislodge the R2 and L2 trigger buttons. There are five screws that hold the controller together. Replace the two on the sides, and the one in the middle. Your controller is now fixed.