With all of the components securely fitted inside the enclosure, it's time to work out what needs to be wired where.
The ATMega328 chip used on the Arduino contains internal pull-up resistors, so we won't need to wire individual resistors for each of the arcade buttons. This greatly simplifies the controller wiring. So all that needs to be done to wire the arcade buttons is to solder one leg to ground, and connect the other leg to one of the digital inputs on the Arduino board.
That said, pin 13 can not be used as a digital input with the internal pull-up resistor. See the pullup resistors section in the Digital Pins article
on the Arduino website for the reasons why. For this pin we'll be using an external pull-down resistor. If you're unsure what a pull-up/pull-down resistor does, check out this great tutorial on ladyada.net
Wiring the potentiometers requires a ground wire, a wire to the one of the Arduino analogue inputs, and a third +5V wire. As the potentiometer is rotated or adjusted, the resistance of the potentiometer changes between the ground and +5V wire. According to Ohm's law, voltage = current*resistance, so with a constant input current and a variable input resistance, the output voltage will be variable. It's this variable voltage that the Arduino reads on the analogue pins.
The attached wiring diagram (created with the great Fritzing
software) shows how to wire up each of the components to the Arduino board. The black wire represents ground, the red wire represents +5V, the purple and orange wires are digital inputs to the Arduino, and the blue and green wires are analogue inputs to the Arduino. Note that the ground wires and +5V wires have been bridged between the buttons and potentiometers.
Before proceeding to the next step you may find it helpful to print out a copy of the wiring diagram to refer to whilst you solder.