When preparing to ship, it is always good and very recommended to wash the vehicle and take few pictures.
When the carrier arrives to pick up your vehicle, he will provide with a bill of lading (BOL) . On the bill of lading you will find the details of the vehicle, the contact information for both pick up and delivery and a drawing of a car from all side. The carrier and you together will inspect the vehicle for any damages or scratches that already existed prior to shipment if at all and mark them on the form.
here is a sample:
As car transport brokers, our job is to insure that the carrier is fully insured and licensed. Upon dispatching the vehicle to the carrier, you should receive all information regarding the carrier including his insurance.
Once the vehicle arrive to the destination, same bill of lading is used for a second inspection. Make sure to go over your vehicle and see there is no new scratches or damages before you sign!
In case you notice a new damage, take pictures and note it on the bill of lading right away and sign you received the vehicle with damages. A signature without any mention of damage is the confirmation you received the vehicle in good condition.
Carriers are fully responsible for any damages during transit (limited to their policy). Carriers usually take care of the damages in 2 ways. If it's something minor, they will fix it them self in a repair shop or ask you to fix it and send them the bill without involving the insurance. If the damage is severe than insurance claim is in order.
With the information you received prior to shipping for the carrier, you will find the insurance details. Contact the insurance agent and file a claim. Insurance company will need the bill of lading and pictures. Once those are processed, an inspector will be sent out to check and appraise the damages. After the inspection submitted his report, you will be contacted by the insurance for the next step. If it's repairable, they will either send you to their repair location or ask you to fix it and send them the bill. If the car is a total-loss you will get a check for the car value as determined by the national lists same as your personal insurance.
In most cases, Insurance work really fast to solve the issue.