Port Vila is small enough to walk across in twenty minutes. For anything further afield, flag down one of the many shared minivans (marked with a B for "bus" on the number plate) — fares are 150 vatu for short hops, more for longer trips. Just tell the driver where you are going.
Taxis (T on the number plate) are more expensive but unmetered; agree on the fare first. To tour the whole island, hire a car for the day from one of the agencies in town. The ring road is sealed for most of its length and an easy drive, though potholes get worse in the rainy season. Drive on the right (a hangover from the joint French–British rule).