Controlling 12v DC Motor with Arduino

I'm looking for a way to control a 12v Motor's direction and turn it on and off. I know how to do it with a 5v Motor by using a relay and two transistors.

Look up H-bridge. Lets you control direction & speed.
L298 for example.

Can find plenty of shields based on this chip.
Really depends on what voltage & current you want to control.