In many cases roofs don't sustain damage from hail and you certainly don't want to file a claim if there's no damage. Your insurance premiums may go up if you file too many claims so it's important to only file a claim when absolutely necessary. Ask to see proof in the way of pictures - it's alright to ask, it's your home and your responsibility.
After the roof specialist has advised you of damage and after you've looked at photos, you will need to file a claim. Filing a claim involves calling your insurance carrier and giving them the storm date.
Once the insurance field adjuster sets an appointment to inspect the roof, make sure the roofing specialist is there to inspect with the adjuster to ensure that all damages are found.
Insurance adjuster will write up the damages with the roofing specialist. The scope of work is used as a guideline for replacement.
With the agreed scope of work between the roofing specialist and the insurance adjuster, the only out of pocket expense should be your deductible. This is why it is very important to use a roofing company that is familiar with insurance specifications.