What is the best way to get from Logan Int. Airport to the Cruise Port?

Am assuming you mean the Black Falcon Cruise Terminal in the Waterfront area getting towards South Boston proper. If so, this is most easily accomplished using two branches of the Silver Line.

Catch SL-1 at Logan Airport and take it all the way into South Station. At South Station, take SL-2 which goes out to the Cruise Terminal.

I'm guessing you will have quite a bit of luggage with you for your trip, so I'd suggest just getting a cab to the cruise terminal. They are easy to catch at Logan. How much time between your landing at Logan and when the cruise departs?

Have a lovely trip.

Agree that taking a taxi is your best bet, though if you want to take public transportation you can take the Silver Line to the World Trade Center (don't have to go to South Station), then transfer to the Silver Line 2 towards the Design Center.

You can check the route on www.mbta.com.

cw, you're right that one can do the line change at the WTC stop, though there actually can be one advantage to changing from Silver Line 1 to Silver Line 2 at South Station. Sometimes, the cars fill up at South Station, depending on time of day and luck of the draw, and you stand a better chance of getting on and/or getting a seat if you change at South Station.