Taking the T from Logan Airport - Boston - TravBuddy

Though taking a cab seems like an easy way to get where you’re going,
there is a cheaper albeit slightly slower way to travel to and from the
airport.
 

To get to the subway terminal, you must take a Massport shuttle bus to
the MBTA terminal. These buses are usually straight ahead when you walk
out the terminal. Wait for a bus which will take you to the MBTA Blue
Line Airport Station. This is a free shuttle bus service to and from
all airline terminals. The Blue Line is your best connection to and
from the Orange Line, Green Line, and North Station, (North Shore and
Points North commuter rail).

Be careful about the Charlie
Card in Boston. The MBTA is switching over from a TOKEN system to a
card system and it's not completely foolproof, be sure to get a Charlie
Card for a few rides, but pay with tokens at the Backbay-Green line
locations. The Charlie Card only covers 1/3 of the subways in Boston.