An analog stick consists of two potentiometers that are used to sense where the analog stick is moving. A potentiometer is a resistor with a third pin called the wiper that moves along the overall path of resistance. As this pin moves it changes its resistance in reference to either side of the resistor. This change of resistance is what the controller sees when you move the stick.  Well, it actually sees a varying voltage that is sent through the wiper but the change of resistance creates the change in voltage.

My modification focuses on these potentiometers. If we remove a small amount of resistive material from the center of the potentiometer, we can make a crude switch that is in an "off" position when not in use. When in use it can connect the wiper to one side of the now broken resistor acting as a SPDT switch. 

On a normal controller when you press a button it closes a signal that is held high to ground. The circuitry in the controller uses this method to know when a button has been pressed. With the modified potentiometers we can run all the button signals (the held high side) through the outer pins of the potentiometer while using the wiper as a common pin that will be wired to ground. 

Now, when you move the stick it'll close a button to ground through the wiper.  

Be sure to watch the video for some horrible gameplay using this beast!