When the at-fault party's car insurance company accepts liability for the accident, which totaled out another vehicle, they are required to make the car owner "whole" by paying actual cash value (ACV) for the vehicle.
Your vehicle's value will be determined by the third-party's insurance adjuster comparing your vehicle, in the condition it was in before the accident, to similar vehicles of the same age, condition, etc. This may include input from local auto dealers, private parties or recent sales as well as using valuation guides like Kelley Blue Book and NADA Guides.
If you had a loan on the vehicle that was totaled out by another driver, their car insurance company will not take into consideration your loan balance to determine the settlement offer. If you owe more the worth of your vehicle (ACV amount), then unfortunately unless you have Gap coverage you will end up still owing on your vehicle.
Besides paying ACV for your totaled out vehicle, the car insurance company may also include in the settlement offer an additional amount to cover sales tax, title and registration (transfer) fees. If they are not automatically offered then you may need to negotiate with the adjuster to get them added to the settlement amount.
The other party's insurance provider may also pay for a rental car for you to use due to the "loss of use" of your own vehicle. Your rental car costs will be reimbursed for the time period it takes them to declare your car a total loss and offer you a settlement amount.
If you incurred any towing or storage fees that you had to personally pay out-of-pocket for, this also may be reimbursed as part of your total loss settlement.
The most you can be paid by the other party's insurer for the total loss is the maximum limit of the person's Property Damage Liability coverage.
If ACV and related expenses exceed that limit, you will still only be paid up to that limit amount by their insurance company. Anything beyond that amount you would have to go after the at-fault driver, for them to personally pay.
If your agent is not able to explain to you what to do in this situation or fulfill your car insurance needs, contact a CarInsurance.com agent and they can explain not only insurance terms and explain claim procedures but also tell you how they can get you low cost car insurance.