If traveling from Boston, you've got a few options:
1. Bus - Take the Peter Pan bus from Logan Airport or South Station to Woods Hole, Falmouth. From there, you will take the Steamship Authority Ferry directly to Martha's Vineyard. It will drop you in either Oak Bluffs or Vineyard haven, where there will be a number of taxis that can take you to your hotel.
2. Car - Drive from Boston to Woods Hole, Falmouth. From here, you can choose to park in the Steamship Authority lots for ~$15/day and take the free shuttles to the Ferry. Otherwise, you can take your car onto the ferry, but be sure to book your roundtrip car tickets for the ferry ASAP as they fill up!
Coming from NYC, you've got a few options:
1 - Fly - Direct flights to Martha's Vineyard airport are the fastest and most convenient way, however can sometimes be fairly expensive. You can also fly to Boston and then take a bus or drive (below)
2 - Bus - Likely not the most comfortable, this is a cost effective way to get from the city to MV. You can take the Peter Pan from NYC to Woods Hole, Falmouth MA. From here, you would take the free shuttle to the ferry.
3 - Drive - Simply drive to Woods Hole, Falmouth. From here, you can choose to park in the Steamship Authority lots for ~$15/day and take the free shuttles to the Ferry. Otherwise, you can take your car onto the Ferry, but be sure to book your roundtrip car tickets for the ferry ASAP as they fill up!