During reassembly, follow these instructions to install the springs onto the R2 and L2 buttons:

Lay the midframe face-down and orient the button properly.

Place the spring over the inside peg with its bent ends facing upward.

Rest one end of the spring in its channel in the button.

Place the button over its clips and rest the other end of the spring in its channel in the midframe.

Press the button's pegs into their clips until they snap into place.