I have found many articles with bad documentation on doing this wirelessly, but I need the Arduino to be wired to the computer.
It's exactly the same. Just skip the part about getting the radios configured/wired/tested/etc.
Forget the PS3 for the moment. How is the joystick connected to the Arduino? What kind of joystick is it?
How do you want the changing values to change the speed of your motors?