If you have collision coverage on your vehicle then you could place a claim against your own coverage in order to get your vehicle repaired. You would need to pay your deductible though. If you chose this route see if your insurance company plans to subrogate with the at fault party. If they do subrogate, then see if they will be able to get your deductible amount back as part of that process.

If you do not have collision or do not want to place a claim with your own insurer then you can usually go after the at-fault person personally to pay for the repair costs. If the person agrees to reimburse you for your repairs then it might be as easy as getting a few estimates to see how much the repairs should cost and then having the person either pay you or the repair shop when the work is done.

If the person does not agree to pay for the damages they caused then you may need to take them to court in order to get a judgment against them for the amount of your repairs and court costs. If you need to file suit against the person you may want to get guidance from a lawyer.