— General Information—
In short, this is a bicycle ride from the Atlantic Ocean, across the US, to the Pacific Ocean. The starting and ending points are in Oregon and Virginia, and you can ride in either direction. I'm choosing to ride East to West.
The "trail" follows the same route ridden by bicyclists in 1976 when a group of people road across the US in commemoration of the Declaration of Independence (Bikecentennial '76). As with many people (most?), i'll be following the maps sold by Adventure Cycling Association (ACA). Their web site has a very good overview of what to expect and instead of simply copying it here, i'll just provide this link.

Very Roughly...
After dipping your bicycle's back tire in the Atlantic in Yorktown, Virginia, you head north to a little north of Richmond, VA, then drop back south again to the North Carolina border (without actually entering the state).
From there you head north again to just below Lexington, Kentucky, and from there ride just about straight west until you get to Carbondale, Illinois. From Carbondale you head west to the Illinois/Missouri border then head south to the MO/Arkansas border. Then it is a west/northwest climb through Missouri and Kansas and into Colorado, with a stop at Pueblo, CO, which is the half way point of the trip.
From Pueblo, you begin a northwest climb through Colorado and Wyoming, up to the northwest corner of Wyoming where you enter Yellowstone Park.
After touring Yellowstone, you enter Montana and continue the northwest climb to the northern-most point of the trip in Missoula, MT, the home of Adventure Cycling Association, the people who make the maps i'm following.
From Missoula, it is southwest through Idaho until you get to about the middle of Oregon (north to south), where you cross the border and ride west through OR to the coast, stopping at the Pacific in the town of Florence.
Some basic facts:
Some highlights from the ACA overview: