The majority of visitors come to the Cayman Islands by plane, arriving at Owen Roberts International Airport on the island of Grand Cayman. The islands are located about 500 miles south of Florida and can be reached in about 90 minutes by air from Miami International Airport. Flights to the Cayman Islands are available from most major US cities as well as from many cities in Western Europe, especially in Great Britain, as the Caymans are part of the British Caribbean. Check the link above for a listing of airlines which serve Owen Roberts airport.
To get to Cayman Brac from the airport on Grand Cayman, travelers can either take a ferry or another small airplane. (Note there is no ferry - 16 seat prop plane or a 737 is your only options with Cayman Airways Express and Cayman Airways). Arrangements for these can, and should, be made ahead of time by you or your travel agent to make your trip as smooth as possible. Flights to Cayman Brac from Grand Cayman are available on Cayman Airways, the Islands' national airline. See their website for travel information.
Once on Cayman Brac, it will be quite simple for you to take a taxi to your hotel or resort as there are many of them available. You may also be able to arrange to be picked up by your hotel's shuttle bus by making reservations with them ahead of time. Call your hotel to find out if they offer this service.