If a drunk driver damages your property or hurts you, they will probably be facing charges for vehicular assault. These charges will happen in criminal court, since driving drunk is against the law.
If you need to pay for your medical bills or other costs incurred as a result of the accident, you may be able to recover damages from your own insurance or the insurance of the driver at fault. A lawsuit filed against the driver or his insurance will happen in civil, not criminal court. There may also be other responsible parties if it is found that the driver was served alcohol at a bar when he should have been cut off due to intoxication.
If you need to recover a large amount of money, it may be time to speak with a personal injury attorney who has a proven track record with helping DUI victims.