Getting around Martha's Vineyard is pretty easy on bike, foot , bus or ... by taxis and rental cars.

Taxis - From arriving airport/ferry terminals

Cabs typically meet any arriving plane or ferry so you should have no trouble finding one.  Cabs themselves are generally large vans that seat 10-12 people.  Good news, they are mostly plentify and relatively cheap (compared to Boston and NYC prices!).  They typically charge a flat rate for the trip which can run up to maybe $15.  Although rates are standard, i.e., there's no real negotiating, you may want to ask upfront so you know what you'll be paying.  Often you'll find yourself sharing with a few other parties headed in your direction.  This is particularly true coming from the ferry terminals.

TIP:  In super-high season, sometimes cabs fill quickly so to look like a local and ensure a seat, you can watch for (or ask a ferry employee where to find) the taxi stand and march right up with your party and your luggage.  State the number in your party and where you're headed and the cabbies will sort you out.  So, "Two for Edgartown" is all they need to know and they will point you to a cab going to Edgartown and help load your luggage.  Once you're talking to your driver, you can sort out where exactly you're going in Edgartown, Oak Bluffs, Chilmark, etc.  BTW, it's not the end of the world if you miss a cab in the first round but you might have to wait until the drivers radio for more cabs.

Taxis - On the Island

If you're staying at a hotel or inn, they can probably help you find a cab.  Otherwise, your best bet is to call for one.  Grab a card from the driver when you arrive or watch in town for any cab with the phone number on the side.  They usually require some notice (10-20 minutes) and, again, particular around ferry time you will often find yourself sharing a ride.  Good news -- people on the Vineyard are pretty friendly and sociable.

Rental cars

Many travelers get around on foot, bike or by bus.  If you're staying at a hotel, most likely you won't need a car or you may choose to rent just for a day or two in order to explore the island at your own pace.  Renting is also a good option because getting a car across to Martha's Vineyard can be difficult and/or expensive (cars require advance reservations that can be difficult to get in high season).

Rental cars are available on the island from a few enterprising local companies, including AAA Island Rentals.  You'll see their open air Jeeps everywhere and it's a fun way to explore if you have the need for wheels and have the cash.  Rental cars are also available at the airport -- Thrity, Hertz and Budget are all there at the time of writing.  Airport code is MVY.  Other major rental car companies may serve the island; it's worth checking if you have a favorite.  Also, if you do call ahead, you can sort out how and whether they might meet you when you arrive.

Mopeds

See Getting Around for more information on mopeds.