You can check here for the rules:
http://www.greatrace.com/events/booklet/05-GAR-2.htm
The basics are that this is a cross country race for vintage automobiles in which each team must pass through various checkpoints as they cross the US. A vintage auto is defined as any automobile over 45 years old with minimal, if any, modifications.
This is not a top speed event. Each stage is a timed, controlled speed, endurance event. Just finishing is like a win for many vehicles.
This years race will run from Philidelphia, PA to San Rafael, CA making it's way through Maryland, Ohio, West Virginia, Indiana, Illinois, Missouri, Kansas, Colorado, New Mexico, Arizona, Nevada, and Utah.
Now for the cost. $5,000.00 entry fee plus other projected costs. $25/day per person for breakfast/dinner costs for 15 days is $750. Lunch is provided free to the driver/navigator team. Fuel at an average of 15 mpg for 4,000 mi at $2.25/gal is another $600. Another $400 for misc. costs brings you in at close to $9,000. Not to mention the cost of actually getting your vehicle to the start line and home from the finish line. Easily $10k if not more. Not a cheap race, but if your vehicle is already worth $25k+ then cost is not much of an issue.
Everything you want to know can be found here:
http://www.greatrace.com/index.php