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MBTA Silver Line route SL1 is currently free when you board at Logan Airport as noted; Massport (the port authority) subsidizes this fare to encourage transit usage. You do not need a CharlieCard or any other payment method to board at the airport; you'll simply be waved on when the bus arrives at the curb, essentially the same as if it were one of the inter-terminal shuttles.
When you arrive at South Station, you will exit behind the faregates (i.e. inside the paid area). You can then ride the T to any point in the system, including free transfers to the Blue, Green, or Orange Lines. You do not, however, get an additional free transfer to another local bus, because your CharlieCard will not have recorded the initial ride.
The ride is not free in the return direction; the outbound Silver Line to Logan is $2.25 with a CharlieCard or $2.75 with a CharlieTicket or cash. Whether the Silver Line or the Blue Line makes more sense, therefore, depends on where you will be traveling from and what your preference of mode is.