Your vehicle will be repaired once the insurance company at fault completes its liability investigation. This investigation includes, but is not limited to, reviewing the police report, speaking with their insured and speaking with the driver. This investigation can take anywhere from a couple of days to a couple of weeks.
Once the at fault insurance company completes its investigation it will either send someone out to do an estimate of the damage to your vehicle or request that you take photos of the damage to your vehicle and send it to them.