The ideal is to rent a vehicle, 4WD if you want to explore the more alternative stretches of Martinique. The island's asphalted road network is good and very comprehensive. Rental vehicle prices start at around €30 per day for rentals of some duration, eg a week.
Although there are larger public buses, most of the transports you will come across are taxis. collectivs which, in addition to being identified with CT, have mentioned the destinations on the windshield. They stop at marked stops. Collectifs taxis charge significantly less, less than €4 for a 45-minute journey.
Only use taxis if you are prepared for prices francophones (read high), paid in euros.