Getting there is no problem at all. In fact, there are so many regularly scheduled carriers, charter flights, tour packages, last-minute savings clubs, etc. that you can be at any number of international airports throughout the Caribbean in a matter of hours. (To confirm that, just check your local newspaper for travel specials).
Once there, you may wish to do some island hopping; "No problem, mon" because airline service within the Caribbean is quite comprehensive. And though you can't always 'get there from here', with a little juggling of some airline schedules and a short hop on those tiny island aircraft, you can always reach your beach destination.
For instance, American Eagle uses the international San Juan airport as its major hub and flies to most islands. And the Caribbean airline LIAT, based in Antigua, promotes two special airline passes to assist a visitor in island discovery; the Explorer Pass costs $199 U.S. and entitles a ticket holder to visit three islands within 21 days while the Super Explorer Pass offers 30 days unlimited travel to more than 21 Caribbean destinations for $369 U.S.
Other scheduled airlines within the Caribbean include ALM (Curacao), BWIA (based in Trinidad), Winair (based in St. Maarten), Air Martinique, Air Mustique and Carib Express.
A warning for nervous flyers: there are certain islands - such as Carriacou, Saba and St. Bart's - which have infamous landing strips, short and scary. In Saba when you 'taxi in,' an overshoot of mere feet could put you off the island runway and into the water. When the plane is approaching Carriacou, they close the public road (which crosses the runway) to vehicular traffic so the plane can land. It is all very exciting. And very Caribbean. ("No worries, mon...")
With all the choice, selection and air passes available, it would be wise to discuss your travel plans and routing with your travel agent - preferably someone who specializes in the Caribbean and has all the airline schedules and connecting flights on hand.
