If you caught the guy, you will need to fill out a form (of accident) and call your insurance broker. If it is his fault, then his insurance company will pay for your repairing bill.
But if you can not prove that it is his fault, then you will have to foot the bill yourself.
It seems you don’t know who did. Just call the police, it was no longer an accident but also a criminal event. The police probably give you a file No and you can fix you car somewhere paid by government.
If the damage is not so serious, fix it and pay by yourself. It really takes time to deal with government.