The only way to get to the Island of Cuba is by Air.
Cubana is the nations national airline. Cubana does not fly to the Untied States but does serve many other countries. It serves a network in the Caribbean, South America, Europe, and Central America as well as Mexico City, Toronto and Montreal in North America, also including domestic destinations.
Other non Cuban Airlines also fly to Cuba.
Aeropostal Air Canada Air France Aero Caribbean Aeroflot Aerogaviota Air Jamaica Turkish Airlines Cayman Airways Cubana De Aviacion Iberia Airlines LTU Martinair Mexicana TAAG TACA KLM British Airways Thomas Cook Airlines Condor  
That is a list of airlines serving Jose Marti International Airport which is the main airport of entry to Cuba.

However you dont need to fly out of the United States to fly to Cuba. Miami International Airport does have frequent service to many Cuban Destinations. Continental Airlines and American Airlines has charter service to Cuba. You must book these flights with a travel agent.