Who is suppose to pay for damage and repairs to my vehicle?
Assuming the other party is at fault for causing the accident, you are entitled to have the other parties insurance pay for the damage and repairs to your vehicle, as long as they have sufficient property damage coverage. The advantage to taking this route is that you will not have to pay any applicable deductible under your policy. The insurance company will send a claim representative to inspect your vehicle and prepare an estimate of the damage and needed repairs. They may give you the option to have the repairs performed at a specific location they recommend OR they may give you a check and you can have the repairs performed at the body shop of your choice. It is important to remember, however, that once you have accepted payment, any additional costs are your responsibility.
You should make sure that you are being properly compensated for the damage and needed repairs. One way to do this is to get your own independent estimate and compare it with the one done by the insurance company. In the event your car is declared a total loss - the insurance company is required to pay you the fair market value of your vehicle at the time of the loss.
You can also decide to have your own insurance company pay for the damage and repairs to your vehicle, so long as you have sufficient property damage coverage to your vehicle. The advantage to using your own insurance company is that it will often be quicker. However, you will have to pay any applicable deductible. If the other party is at fault, your insurance company has a right of subrogation (that is the right to get paid back by the at fault parties insurance).