Depends on the car, but I've shoot with many. Some have a flat front, so that you can fit two legs of the tripod on the bumper and then bungie through the grill or a popped (but not up) hood. I did this with an old Chevy Malibu. A cool touch was driving up to a waiting cameraman, who then panned the camera to follow me walking, after it filmed me driving.
I've also shot on sports cars (Trans ams, Camaros). For those, I put a blanket on the hood, then lay the tripod flat (you need a head that can tilt from that flat position - like my Gitzo can). I put sand sacks on the tripod to keep it from bouncing, then tie everything down. My Gitzo tripod extends to the point where I can even shoot through the side windows, so I can get left, right and front angles. Camera on the outside, mics inside. You can use a polarizer filter to cut down on windshield reflection or glare.
Nowadays, you can also use a GoPro, which can go just about anywhere.
I have also done greenscreen, but I prefer really doing it. Driving shots, done well, can add nice production value.