By plane
Bahamasair (http://www.bahamasair.com/) offers a comprehensive network radiating out from Nassau and covering most population centers. However, fares are expensive, frequencies are low, planes are small and the airline is notorious for extensive delays, and many travellers in a hurry opt to charter planes instead.
By taxi
Taxis are very expensive. A short ride from the airport to Cable beach costs $18, to downtown is $26. Between Cable beach and downtown expect to pay $15-$20 with no room to negotiate.
By bus
Nassau/New Providence have a system of buses called jitneys, discussed in the Nassau article. Bus travel on the other islands with the exception of Grand Bahama is very limited.
By Boat And Yacht
Mail boats serve almost all populated islands in the Bahamas, and are amongst the cheapest way to reach many areas, though far from the fastest or most comfortable. The government has a mailboat schedule of mailboat routes online (http://www.bahamas.gov.bs...) which may or may not reflect reality.
Windward Islands (http://www.windward-islan...) - (http://www.alquilerdeyate...), a yacht charter company, can take care of all charter requirements, from bareboat to crewed yacht in the Bahamas starting Abaco.