So here's the condensed version...
To drive well, you need the skill Drive I. Without it, you might crash.
Driving rolls are Agility/Level/Luck, modified by weather, terrain, condition of the vehicle, and handling of the vehicle. See the TRP (total running performance) chart for the condition modifier, and see the vehicle's stats for the handling modifier.
Max speed is based on the vehicle itself and the condition it's in. Multiply your TRP % by your vehicle's max speed to get its current Max Speed.
You can accelerate and brake. If you want to accelerate harder or brake harder, it'll take an action or a full-round action, and maybe a driving roll.
-4 to attacking while driving, and everyone else in the vehicle gets a -2, unless you've got skills that negate this.
If your vehicle gets damaged, the TRP goes down. If TRP or HP go to 0, the vehicle stops working. Damage to the vehicle's armor doesn't hurt your TRP.
Tires are an easy target. They have less HP, and if you lose enough of them, you'll have to make driving rolls not to crash.
You can crash, and you can ram people, objects, walls, or other cars. It'll hurt you, your car, and the other person, object, wall, or car. And it's worse if you don't wear a helmet or buckle up.
For more details and reasonings, please read the longer version of the rules.