you'll need to connect the 5v power wire from the P360 to the red wire on one one of th e4 pin molex connectors. In case you don't know what connector i'm talking about, there will be about 3 or 4 connectors on the Power supply that are the same. They should have a yellow wire(12v), 2 black wires(grounds), and 1 red wire(5v).
As far as the rest of the wires on the joystick, you hook them up just as you would any other joystick(or the joysticks you're replacing?). Hope this helps.
-Kevin