Option 1: The insurance company for the party at-fault should pay for the repairs. However, sometimes they will want to investigate the accident before agreeing to pay for the damage to your car. If it appears that they may take too long to investigate and you need your car repaired sooner then consider Option 2.
Option 2: If you have Collision Coverage, you can opt to have your own insurance repair your car, typically less a deductible. If you choose this option you will ultimately get your deductible back from the at fault party’s insurance.