There are several flights a day between Havana and La Isla de la Juventud with national carrier, Cubana (http://www.cubana.cu).
Cayo Largo del Sur is served by regular charters from Canada and Italy. There are also regular charters to/from Havana.
There is at least one boat a day between Nueva Gerona on the Isla de la Juventud and Surgidero de Batabanó in Mayabeque province with an onward bus to Havana.
There is no boat service between Cuba's Isla Grande (mainland) and Cayo Largo del Sur.