Getting around Lanai requires either your own two feet (in Lanai City) or a four-wheel-drive vehicle (everywhere else). There is no public transportation anywhere on the island.
Lanai City is small enough to walk entirely. The town covers only a few blocks and the main attractions — Dole Park, the restaurants, the shops, Coffee Works — are all within easy walking distance of each other. If you're spending a day in town, leave the car parked.
4WD rental is essential for reaching the best beaches and sites. Shipwreck Beach, Polihua Beach, and the Garden of the Gods all require driving on unpaved dirt roads that a standard car will either refuse to complete or damage attempting. Dollar Rent A Car and the Four Seasons both offer 4WD vehicles on island — availability is limited, especially in peak season, so book well in advance. Rates are high by mainland standards; factor that into the trip budget.
The Four Seasons operates a shuttle between the resort and Lanai City for guests; day-trippers arriving by ferry are met by resort vehicles if they have reservations, but independent travellers are on their own.
A handful of taxis operate on the island, but they are not reliably available and should not be counted on for exploring beyond town. If you're arriving by ferry without a vehicle reservation, confirm your transportation before you leave Maui.