To repair the car, you'll need two items: A gas canister and a car battery. You'll also need a set of car keys to start the car and escape. There will be at least two of each of these items around the map, so they should not be very difficult to find.
Once you have one of the parts, you'll need to find a car. There are two cars on each map; the blue car seats four counselors and the yellow car seats only two. Once you've found your car, take the part to it and install it. The battery will go in the front of the car and the gas in the rear. Begin installing the part by holding A, which will initiate a short minigame where you need to press either LB or RB as the meter passes the highlighted areas. Failing to press the correct button will cause a delay, but also make the sweet spot larger. Characters with higher intelligence will have both a faster-moving meter and larger sweet spots.
After the car is repaired, the player going for this achievement needs to find or pick up the car keys, then move to the driver side door and use the keys to get in and hold A to start the engine. Once the engine is started, passengers can get into the car; three can enter the blue car as passengers but only one can enter the yellow car.
In order to escape, the driver will need to navigate the car out of one of the camp exits in the northern corners of the map. A map will help you find them, but if you do not have one, just following the roads will eventually lead you to one. Do not attempt to run Jason over - he will destroy your car if you hit him. Instead, swerve around him if he tries to block your path.