I'd suggest to make your circuitry work. What's the use of a motor shield with a servo? A 9V (block) battery is too weak for driving a motor, get a stronger power supply.
Then make the servo follow the pot, using the Knob example of the Servo library.
Once you got that working, add a PID controller. Either use the PID library, and follow the instructions and code examples, or roll your own PID code.
A servo motor already includes a PID controller, what difference or improvement do you expect from an additional software controller? For other motors you'll need feedback from the motor, about position or rotation, as input for a PID.