Controlling an RC Car's remote with a Mega 2560 board

Those are just the basic Bring-to-ground controllers. If a button is press, it is brought to ground and the chip sends out the appropriate command.

Since the arduino only has high and low output (5V/0V), those chips can only take about 2 - 3V, so I would recommend using a transistor and instead of wiring directly to the contact points, use a transistor to simulate a button press.