By plane
Nassau's Lynden Pindling International Airport IATA: NAS, ICAO: MYNN is the largest airport in the Bahamas. Most major U.S. airlines with the notable exception of Southwest have flights to Nassau. Limited service from Toronto and London also exists.
The two most popular Fixed Based Operators FBO located at Lynden Pindling International Airport are Executive Flight Services and Odyssey Aviation. Air taxi and air charter companies such as Jetset Charter (http://www.jscharter.com) fly a variety of private charter aircraft and jets, from charter luxury Gulfstream's down to economical piston twins for small groups and individuals into and out of Nassau.
The airport itself has seen better days, but the free drinks occasionally served on arrival and the live band serenading the Immigration hall help set the tone. No public transport is available at the airport, but there's a list of fixed taxi fares posted at the exit. It's about US$25 and 10 mi 16 km to most hotels in central Nassau.
On the way back, note that there are three terminal concourses: domestic and charter flights, flights to the US, and non-US international flights. US Immigration/Customs preclearance can be very time-consuming, so show up at least two hours before your flight. Security for other destinations is considerably more laid back, and an hour should suffice.