To get started, turn left as you leave the office and click on the old black & white car (labeled "DeSoto," a Chrysler model popular with law enforcement in the 1950s) in the alley. You can't use the car in every episode, and in some you can't use it until you need it; so if you click on the car and nothing happens, try later in the game when there's a specific place you want to go.
When you're driving through the city, the street is endless, the other traffic absent or irrelevant, and the DeSoto invincible, so go ahead and hit anything you want. You can also steer for the occasional ramps if you want to make the car flip. You don't get any points for this, but if mindless destruction makes you happy, have fun.
To move around on the road, click where you want to go and Sam will swerve over there. It's not graceful, but it gets the job done. If you want to shoot at something, click on the gun icon at the bottom left; if you want to pull someone over, click on the bullhorn; if you want to honk the horn, click on the horn. Just like a real car, isn't it?
When you're done, click on the house icon at the bottom right to return to the neighborhood.