Grab a working R/C car, not the cheap toy ones but one you'd find in a Hobby Shop. Pull out the RC receiver and replace it with your Arduino.
Code, rinse, repeat.
To your Arduino a typical RC car "looks" like 2 servos. A throttle and Steering. Your ESC, or speed controller will supply you your 6V to power the brains and servos of the machine.
-jim lee