Instructions
Get a car. You can do so by carjacking, stealing a parked car or getting in any cars that may be in your garage.
Take you car to one of the five car modification places in the city. There are two in the Los Santos area, two in the San Fierro area and one in the Las Venturas area. Keep in mind that the "Wheel Angels" in San Fierro only modifies street racing vehicles, and the Loco Low Co. in Los Santos only modifies low-rider vehicles.
Modify your car. Depending on the car you brought in, you can add a number of features to it, such as hydraulics, new paint jobs, spoilers, hood vents, roof scoops and many others. All of these modifications will cost money, so you will need to make sure you have enough to modify the car to your needs.