You should contact your local law enforcment and file a police report and give them the contact information for the other driver.

Once you report the damages to the insurance companythey may offer to subrogate the damages. So, instead of going after the other driver directly, you go through your own insurance company. As a result, you give your insurance company the right to go after the the other person to collect their costs. Normally since you are paying through your own insurance policy you will have to pay the deductible, but the insurance company may include the deductible when they collect it from the other driver and reimburse you later.