Here the hardware diagram of the arcade button.
Wiring the arcade button for input into the Raspberry Pi is as follows:
The two connections on either of the arcade button's long sides are for powering the built-in LED. These connection are seen on the bottom left, in the diagram above. Connect these to the Raspberry Pi's power and ground sources if you want the LED lit.
The connection on the very bottom is wired to Ground on the Raspberry Pi. This connection is seen on the bottom-right side off the diagram above.
The button connection that sticks out of the housing, in the same direction as the Ground connection, is connected to pin 13, on the Raspberry Pi model B Revision 2, pin header. So if looking down at the Raspberry Pi with the header in the top right corner, then the input pin connection is to 7th pin down on the left side.
Here is the wiring diagram for the project: