To get to Virgin Gorda you can catch a scheduled flight from San Juan, Puerto Rico to Tortola, then take a taxi to Trellis Bay where you can catch a ferry boat over to Virgin Gorda.  Cape Air, American Eagle and Air Sunshine provide scheduled service to Tortola.

The only way to fly directly to Virgin Gorda is to charter an airplane or helicopter from one of the few airlines approved to land there, such as Island Birds or Caribbean Buzz Helicopters. They can fly you directly to Virgin Gorda from San Juan, St Thomas, Antigua or St Maarten. 

There are several ferry services that transport passengers between St Thomas and the British Virgin Islands.   Check out the schedules and prices if you decide to fly into St. Thomas and ferry over to Virgin Gorda. It is a long and often very bumpy ride, however a cheaper option than flying.
Speedy's Fantasy   - connects Virgin Gorda, Tortola and St. Thomas

Inter-Island Boat Services - connects St. John and Tortola

Smith Ferry Services   - connects St. Thomas, Virgin Gorda and Tortola

** Note:  Some of the original information for this thread came from the following forum thread: