In a rare display of foresight, all forms of motorized transport are banned from the islands: your only choice is horse-drawn carts, known as cidomo, which are used even to shuttle around diving gear. The price for visitors is Rp 20,000-30,000 per head for any trip, although it varies per island and per season. However, as the islands are only a few km in diameter, it's entirely possible to just walk instead.
Bikes are also available for rent, but be prepared for as much walking as cycling as your tires spin-out in frequent stretches of sand.
Travelling between the islands requires either catching the infrequent scheduled Koperasi Island hopping boats, or chartering one to take you across. You can buy tickets from the ticket offices on each island from where the boats depart. Booking through a travel agent just costs more, and you still need to change the reservation to an actual ticket at the very same counter.
The distances between the islands may seem swimmable, but do not attempt it — the currents are fierce and several foolish visitors have died trying.