The purple left and right pads feature "little slots" that snap into "registration keys" that are located on the back of the top half of the case. These four notches were designed to have a very tight fit and lock into the nubs.
Install Left Pad
Start with the left pad (this one fits over the analog thumb joystick). Line up the registration slits with the nubs on the top half of the case. Orient the part so the quarter sized circular notch lines up with the center standoffs. Firmly press down on the part until it clicks into place.
The two button covers can be pressed into the recessed areas on the right purple pad. These should have snug fit and click into place. Optionally add some adhesives if you find them come loose.
Install Button Actuators
The four colored button actuators are inserted into the four holes on the back of the purple right pad. The button actuators has a flange that prevents them from falling through the hole. The actuators should have a loose fit which is necessary for the buttons to be pressed without getting stuck.