Remote controlled lights
I used to use gamepads as input device for USB many years ago. I simply soldered wires paralel to buttons and shortcut them to "simulate" the button press - it worked nice and reliable.

With Arduino - I would measure the voltage on the button in question with Voltmeter - if the voltage is less then Vcc of Arduino (5Volts), I would simply connect Arduino ground to lower side (negative) of the button and output pin to the high side of the button. Then I would set that pin for Input to have the button released (from Arduino side) and to LOW + Output to have it pressed. (maybe I would first shortcut the button with Ampermeter to see, that no more, than 100mA is sinking there).

If the sink is more, or the voltage is more, then I would use relay and shortcut the button with the relay, switching the relay with Arduino.

( something like this http://www.instructables.com/id/Home-Automation-How-to-Add-Relays-to-Arduino/?ALLSTEPS )