Bumper cars are powered by electric motors, and as you may know all electric devices require a complete circuit in order to operate. In the case of bumper cars, Electricity flows in a circuit - if you look at old bumper car setups, you’ll notice that each bumper car has a metal pole on it with a wheel that touches the metal mesh ceiling, and the floor of the bumper car ride is metal too. The electricity flows from the ceiling, through the little wheel, down a wire in the pole, through the electric motor, and completes the circuit through electric contacts under the car (A wheel or a small metal brush), into the floor. If you look up, you’ll often see the little wheel sparking as it rolls along.
The pedal on the floor of a bumper car is a simple on-off switch for the electric motor.
Bumper cars don’t steer the same way that normal automobiles do. Bumper cars have a front wheel that can do a full 360 degree turn - so if you turn the steering wheel a little bit to the left, the car goes forward and turns left. Turn the wheel more to the left, and the car will spin around in a circle. Turn the wheel even further to the left, and the car goes backwards. Other than that, bumper cars just don’t go too fast, and they have large rubber bumpers that absorb the impact when you crash in to someone else, so you (or the car) don’t get hurt.
Unless you’re really tall, you won’t get a shock unless you touched the ceiling and the floor at the same time - and dry human skin and the soles of your shoes provide enough electrical insulation so you won’t get a shock. Bumper cars use the same principle as electric trains with overhead wires - the source of electricity is high up in the air, reached with a special metal pole, and the electric current return is the metal rails under the car.
Sadly, bumper cars will ONLY work in the bumper car arena, you can’t drive a bumper car out from the bumper car arena and drive around the amusement park.