All you have to do is drive 10 kilometers in any vehicle. The following guide will tell you how to get the first car.
Once you get to the life guard post/house/whatever you want to call it, you should get the mission that allows you to unlock the truck. You'll find the start to the mission on the bottom floor of the house, there should be a man next to the truck. Talk to him to start the mission. All you have to do is find 4 broken down cars and take a part from them. Just run up the street, killing any zombies you encounter. You should find 4 cars pretty easily. Go up to the front and hold down X to take the car part. Once you have the 4 car parts, take them back to the mechanic, who, after completing a mission, will give you the truck. Then just have fun driving around, the game should give you updates for every kilometer you drive.