First take the details of the owner of the car if he is not ready to take responsibility. Then get in touch with the person or his insurance company. From there, his insurance company will conduct its own investigation to determine if he was the one on the wrong.
Sadly I've heard this is a common mistake- that usually doesn't hold much in claims suits. The law states you are responsible for your vehicle & u cannot trust another car to give u the right of way. Although if the person hit u from behind or on your side, they can be held accountable if they were supposed to stop or yield to your vehicle. If u rear-ended someone however, it is almost always marked as your fault. Ask your insurance agent to help u determine fault & don't make a claim unless the damage price of your car is over your deductible charge. Just in case the other car doesn't have insurance. Sometimes you'll pay & not b compensated if so. Best of luck!