Occasionally there will be time in pre-production to discuss what car your character will drive, but more often the decision will be made based on practicalities; what period the film is set in, whether the car has to get involved in a crash/accident, the cars the other characters are driving and, no doubt, what deals the production can get.
Whether or not the actor can drive, there will usually be a stunt driving double. This will save the production money; when the actor is working on the main unit, the second unit can film driving scenes. If the actor can drive, and has a valid driving license, they will perform most of the driving scenes themselves, but there are plenty of ways to make it look as if an actor is driving. If the camera is very close and the car just rolls into shot, you can be pretty sure the actor doesn't drive and several crew are crouched behind the boot hoping the actor doesn't reverse either.
The most common shot you will see is an actor getting into a car and driving off or pulling up and getting out. If you're watching a cop show or movie, you'll see that a lot. They can take a while to film. The actor might never have driven the car before and will go on a test run with the stunt driver or the car owner/driver. Local police officers will be controlling traffic as only they are permitted to do so. The visual effects department will have set up any rain/snow machines and the Director of Photography will have lit the inside of the car and the street, if it is night (characters like to drive with their sun visor down and the interior light on). There will be some form of microphone in the car, if not an entire sound recordist squashed in the foot well.
There are certain hurdles for the actor to clear in these scenes, primarily one of timing. The set ups are narratively necessary but rarely of interest in themselves, so they can't be lingered over. The reality means getting to the car, unlocking it, opening the door and getting in, putting on seat belts, starting the car, getting into gear, indicating etc, pulling out. Costumes, mud, props and combustion engines can all conspire against you. If you are pulling into the shot, then you will also have a critical stop mark. Above all, being a girl driving in front of a predominantly male crew, you will not want to stall.
There are plenty of other ways of filming with cars. A low loader places the car on a flat bed truck with room for the camera and crew. Cameras can be attached to the sides of the car, or the camera operator, and focus puller, might sit in the car with the actor. Rear screen projection inside a studio is not used much anymore, if it is it will usually be in an ironic, 'homage' way. If there has been a stunt shot, you will have to do close-ups, probably parked outside the studio while someone screams "left, right, spin, hit the window with your head!". Driving stunt doubles for women are thin on the ground, so actresses will spend days doing close-ups of accidents to cover for the large man with an ill-fitting wig who performed the original stunt.
When I was filming 'Heartbeat', I drove a rather beautiful but ungainly, Citroen Safari. It was very low slung but in immaculate condition and felt like what I imagine driving a hearse might be like if you were allowed to do 40mph on a country lane. At least it had synchromesh gears. On 'A Summer Story', I drove a vintage 1930's car (I cannot recall the make). It had to be double-declutched to change gears, a process involving much footwork and more arm strength than I can easily access. We were filming on Exmoor and had run over schedule and at the end of the film I was left with the second unit, bombing on my own round the National Park like Mr Toad. So reduced was our crew by this time that when we finished a long shot, the traffic was mistakenly released before I returned to base. The lanes were one car width, edged by dry stone walls, the brakes were heavy. To all the tourists I met on my way back, I can only say, Sorry.