You are responsible for booking and paying for your travel to Williamsburg.
The three airports closest to Williamsburg are in Richmond (RIC), Newport News (PHF), and Norfolk (ORF); Richmond and Norfolk are about an hour away by car, and Newport News is about 20 minutes away. There is also an Amtrak (train) station close to campus with service from Washington, D.C. and other major cities on the East Coast. The Reves Center website provides more detailed travel information about getting to campus from these airports.
Please be aware that you will not be able to move in to your dorm rooms before your designated move-in date, so if you arrive early, you will have to make your own arrangements (the link above will also take you to a list of local hotels).