If you have been involved in a car accident with an uninsured driver, if you selected uninsured motorist coverage, you can sue your own automobile insurer for any damages caused in the accident. If you did not select uninsured motorist coverage, you can file a lawsuit for your personal injuries against the uninsured driver for your pain and suffering and any medical bills caused by the accident, but whether you can collect those damages will depend on whether the other driver has sufficient assets.
Following the accident, gather as much information as possible, by taking photos and videos of the scene. If there are any witnesses ask them if you can record a video of them stating what happened. If the other driver has fled the scene, try to record as much as you can that could help the police find the vehicle. Any parts of the license plate, make or model, color, style, and any type of description of the driver could help.