Car with liability hit by unisnured driver, how to get money back?

My car is insured with liability. It was hit by an uninsured 1992 Buick on April 27. I definitely have no responsibility for this crash. The right front door and around area were seriously damaged. The estimated cost of reparing is $2300. The police invesigated the accident on scene and gave me a report. The uninsured driver's plate no., license no. and address were on the report but no phone number. How should I do to get the money back? File a suit in the county court? Hire a lawyer? Thanks.