You have to either compete in car shows or some form of racing. Most companies don't mind if you have other parts on the car as long as you have some of theirs. Like for example if you have Falken tires then it's not like those are the only parts you can put on your car.

Usually the way you get sponsored is to go to a company and say, "hey look, I have your parts and I'm doing these car-related events, I think I can get you guys exposure, blah blah blah."