The best transportation option on Martinique is to rent a car. There are numerous car rental agencies at the airport that can set you up. Be aware that many companies offer a rate that adds on an extra charge for every km you drive. Your home driver's license is valid - as is driving on the right. Motorcycles can also be rented.
Public transportation, the cheapest transport option, consists of buses known as taxi collectifs. One of the most useful routes runs between Fort-de-France and Saint-Pierre. It runs frequently on weekdays, less frequently on Sunday, and takes about 45 minutes. Taxis are more convenient but considerably more expensive.
There are a couple of regular ferries (vedettes) running between the main resort area of Pointe du Bout and Fort-de-France, providing a good alternative to heavy bus and car traffic and city parking hassles - and they're quicker to boot.
Martinique's only commercial airport is in Lamentin, 9km (6mi) east of Fort-de-France. The airport is just a 10-minute ride from the capital and about 20 minutes from the Pointe du Bout resort area. Taxis are readily available at the airport but are expensive, so if you plan to rent a car during your stay consider picking it up at the airport. Because of the taxi union, there's no direct bus service from the airport.