The Steamship Authority ferry from Woods Hole on Cape Cod is the standard way to reach the island; it takes 45 minutes and is the only ferry that carries cars. Book vehicle space well ahead in summer (months ahead for July and August); foot passengers can usually walk on.
Seasonal passenger-only ferries run from Hyannis (Hy-Line), New Bedford, Falmouth, and even New York (the Seastreak high-speed from Manhattan in summer). These are quicker and more pleasant for foot passengers.
Martha's Vineyard Airport (MVY) in the middle of the island has seasonal commercial flights from Boston, New York, Washington and a few other east-coast cities, plus year-round Cape Air service. Most flights are small turboprops.
Once on the island a car is useful but not essential. The Vineyard Transit Authority runs a flat-fare bus network in season, and cycling is excellent on the network of paved paths between the down-island towns.