State insurance laws differ, but normally if the other party is at fault then you can place a claim against their liability property damage portion of their policy for the damages you sustained. Liability Property Damage normally would pays for damages to your vehicle, up to the limits of the at-fault party's limits.
If the current actual cash value (ACV) for your vehicle is less then or near the amount of the cost of repairs to your vehicle, then the insurance company's claims adjuster may declare your vehicle a total loss. If you vehicle is determined to be "totaled" then you would receive ACV for the vehicle instead of the insurance company making repairs.
If you have not yet made a claim with the at-fault party's insurance company for your vehicle you should be able to do so by calling them with the other party's insurance number and reporting the damages. For more information on how the auto insurance claims process works read our article on how to Settle Your Insurance Claim.