It depends on what state you live in. To protect yourself, you should have reported the accident to the police to make sure there is a record. Contact your local division of motor vehicles and ask what is the procedure in your state.
Next, get estimates on having it repaired. Present him with the bill and see what happens. If he refuses to pay, you can sue him for the cost of fixing it, If his failure to have insurance is a violation of state law, that is additional leverage to insure he pays. In most states, operating a vehicle without insurance is a serious offense.