[Alan Anderson]

Do you know how to make the motor run? Do you know how to read the encoder? Can you figure out what encoder value represents the desired motor position?

If you start the motor when the joystick button is pressed, and stop the motor when the encoder indicates that you have reached the target, that might be enough. What motor are you using, and what is it connected to (gearbox, sprocket and chain, direct drive of a mechanism, etc.)?