Getting around Martha's Vineyard is pretty easy and, as an Island, by definition it's difficult to get too far off track!  In particular, most people visit the island and never need a car or any type of formal map.  Most people get around by foot, by bike, by scooter/ moped or by tourist-friendly public transport.

By foot

If you're visiting any one town and staying at a hotel, it's likely that you will find yourself within walking distance of a shopping area, art galleries, restaurants and even a beach.  Frankly, most towns restrict bikes, rollerblades, etc. in the town center and parking is often difficult.  There are also extensive bike trails for longer walks or jogging for exercise.  For family travelers, it's worth noting that these bike trails are almost all paved and are very easy to navigate with a jogging or more conventional stroller. 

By bike

Bike rentals are plentiful and bike trails extensive.  Bike rentals include helmets and you can rent accessories if you're traveling with kids (whether it's a bike tandem/extender so they're attached to your bike or a buggy for smaller kids).  Bikes are great for taking in the scenery or riding out to any of the "out of town" beaches or local farms. 

If you're biking for the sake of biking, note that a healthy adult can bike between the major towns without too much trouble.  In particular, the roads and trails between Oak Bluffs, Vineyard Haven and Edgartown are all pretty easy going and generally flat.  For trips up island (Chilmark, Gay Head) or out to Chappaquidick (seashore/national park out on the tip), you may want to gauge distances before you set out and judge your own fitness. It's doable but the weekend warrior might be pretty tired out.  Definitely bring water, hat, sunscreen, bugspray, etc. as there are long back country stretches without any stores or services of any kind.

By scooter / moped

Although mopeds (and inexperienced, irresponsible drivers) are the bane of the locals' existence, they are pretty fun way to see the island!   It is recommended that you travel in small groups, pull off the road if you have any trouble or are lost (don't just slow down and point and weave!).  By law you have to wear a helmet, obey traffic rules & regulations and stay off the bike paths.  Rental shops are available in all the major towns and typically priced by the day or half-day.

By bus

Martha's Vineyard Transit Authority has really stepped up its visibility and accessibility to tourists in recent years.  Although no doubt locals ride the bus, the transit authority has made it ridiculously easy to understand the bus routes and use the bus to get around the island whether it's from town to town or out to the more remote beaches.  Fares are cheap, estimated at no more than $2 for any trip across the island. 

It's worth noting that in most towns, the bus stop includes a shop for sundy traveler needs (sunscreen, hats, bug spray, cold drinks, postcards and stamps).  These bus stops are often the only public restrooms in the town as well so you may want to take note of where they are located even if you don't ride the bus.