Ubisoft is hosting a closed beta for The Crew starting September 30 through October 4. It's unclear how Ubisoft will select participants for the beta, but you can sign up at the game's website.
In the beta you can explore the entire United States (with no loading screens) and participate in various missions and skill challenges, as well as free roam. Beta players will also have access to two PvP lobbies where they can compete against other players on courses in the US Midwest and East Coast.
Before the game launches on November 11, Ubisoft has said what you'll see in the beta for The Crew is not representative of the final game.