Exuma International Airport (GGT) sits about ten miles north of George Town. American Eagle flies direct from Miami up to three times daily, and Delta serves George Town from Atlanta several times a week. Bahamasair runs twice-daily flights from Nassau (about 35 minutes). Air Canada has seasonal service from Toronto.
From Nassau, Bahamas Ferries operates an overnight service to George Town (around 14 hours, $130 return for adults). It is slow but scenic if you have the time. The mail boats MV Grand Master and MV Captain C also sail from Nassau several days a week, stopping at various Exuma Cays including Staniel Cay, Black Point, and Barraterre before reaching George Town.
For the Exuma Cays specifically, Staniel Cay has its own small airstrip with charter flights from Nassau (about 30 minutes via Flamingo Air or Titan Air).