Most home insurance companies use the following process.

The insurance company sends out their adjuster to inspect your roof for hail, wind, or tree damage. They mark it with chalk and take pictures. TTCR likes to be on-site with your adjuster to make sure everything is examined.
Your insurance adjuster will send a report listing all the damage, what they want fixed or replaced, the total dollar cost of the roofing job, the ACV (actual cash value) of the job, the depreciation, your deductible, and how they will handle payments.
Usually the insurance company will send a check made out to you and your mortgage company.