There are good transport connections in Fiji making internal travel easy and relatively inexpensive. Clearly, the most expensive way to travel between islands is by plane, and there are many domestic operators servicing all of the island groups, but unless you've got no time and heaps of money you're probably better off looking at ferries and small local boats.
Ferries are inexpensive, frequent, reliable and very seaworthy, and rubbing shoulders with the local people while travelling between islands is a pleasant and interesting part of the Fiji travel experience. Ferry routes connect most major coastal areas of Viti Levu and Vanua Levu with all the major islands. You can charter boats as well, or catch one of the smaller unscheduled local boats between islands (although the latter are best avoided in heavy seas).
The larger islands have good bus networks, and outside the towns you can often just hail down a bus wherever you see one. Express buses travel between major centres and local buses seem to stop at every village they pass, but by either means bus travel in Fiji is a pleasant way to meet local people and an effective way to get around.