There are two ways to get to the island: take a flight, or choose from many boat options from nearby coastal towns.
Hvar Island does not have any international airport of its own. The closest local and international airports are in the mainland, in Split, Dubrovnik, and Brac. If you wish to reach fly down to Hvar you can board on a seaplane, services offered by European Coastal Airlines.
Many options are available to reach Hvar, such as ferries, catamarans and yachts from the town of Split. You can also get your rented car transferred to the island trough ferries.
There are a few bus connections around the island which mainly connect Starigrad, Jelsa and Hvar town. However the best way to commute and explore the island would be to rent a car, scooter or a moped from local rental service providers. You can also hire taxis from the ferry port but they are surely going to charge inadequately a lot. Another way to measure the waters around is to hire a water boat through UberBoat.