Search online or in your local phone book for auto transport companies. Usually you will be able to obtain an estimate online or over the phone. It's best to get several estimates and to resist the temptation to go with the first place you call. What you can learn from a brief conversation with a company representative can tell you volumes about the character of their service.
Choose whether you want your car to be shipped, saving it from the added mileage, or driven, which will most likely be faster and more expensive, but will save you the costs of purchasing extra insurance and having to prepare the vehicle for shipping. If you do choose to ship the car make sure to purchase insurance should it be damaged.
Inspect your vehicle yourself before leaving it with the company. Remove any valuables from the interior and trunk to avoid any conflict should something be missing when the car arrives. Take pictures of the interior and exterior of the car for your records. The transport company will also inspect your car, but it is best to have your own copies for reference. Take the car to a mechanic and have him certify what kind of condition it is running in and make a note of any aberrations in its performance.
Inspect the car upon its arrival for any damage. Start it and drive it for a minute or two to ensure it is in the same condition as you left it. If there is anything wrong immediately contact your insurance company and notify the transport company before you sign any documentation that you accept the car and potentially waive any rights to sue for damages.