Tinian is a small island — roughly 18 km long and 8 km wide — and most of the main attractions are spread across it, so you will need wheels. Rental cars are available from a handful of agencies near the small terminal; rates are modest and reservations are advisable since supply is limited. Scooters are another option and well-suited to the quiet roads. There is no public bus service.
Taxis exist on the island but are scarce. If your hotel or guesthouse can arrange pickup from the airport or ferry pier, take them up on it — flagging a cab is not straightforward. Many visitors coming from Saipan for the day hire a car on arrival and return it before their afternoon flight or ferry.