Swapping 5V and GND for a 2 wire motor I have a 2-wire brushed DC motor in a servo housing which either pushes left or right (and "center" when unplugged).

To push to one side I connect a wire to 5V and the other to GND, to push to the other side I just need to swap the wires.

How can I achieve this with the arduino without any physical rewiring?
I think you need arduino motor shield.



Click Here

Just click on above link, you find a good tutorial about arduino motor shield. I hope it might be helpful.