The only time your vehicle should be driven during transport is when it is being loaded on and off the carrier. (This may also be necessary while in transit in order to move other vehicles on or off the car carrier.) Otherwise, it will remain on the truck until it has reached its final destination.
If you are using terminal-to-terminal shipping, your car will also be driven from the terminal onto the truck and from the truck to a parking location at the destination terminal.
In total, your car should only be driven 1-2 miles during auto transport. If you are concerned about it being driven more than that, you can check your mileage on the odometer at drop-off and pick-up to be sure.
Driveaway service is very different from shipping your vehicle. With driveaway service, a professional driver drives your vehicle between your origin and destination. To estimate the distance that will be driven, you can use a mapping software (such as Google Maps or Mapquest) or request a quote from the service company.
MoveCars.com is a comprehensive online directory of car shipping companies, including enclosed auto transport and international shipping companies. Even before you start looking for a car shipping company, you can find answers to frequently asked questions (FAQs) about car moving, car shipping tips, and a glossary of auto transport terms.