You can either take a taxi or public transportation if you don't mind making a few switches along the way.
The MBTA's Silver Line is right across the street. The Silver Line is a bus that takes you to South Station which is on the Red Line of the subway system. Unfortunately Charlestown is a little corner of Boston so you would then have to take another train and another bus to get to the Charlestown Navy Yard where the Constitution is docked. The one good thing about that is once you get a Charlie Card (it's a card that you put money on to travel on the public transportation system) you can transfer from one mode of transportation to another and only pay once as long as your initial payment is more expensive than the next one. In Boston the train is more expensive than the bus so if you take a train first you transfer to the bus for free. If you go the other way, bus to train, you just pay the difference.
It sounds kind of complicated but if you are from a city where you are used to public transportation than you won't have any problems.
One of your other options would be to take a taxi to Faneuil Hall Marketplace. From there you can take a trolley tour (Old Town Trolley if you want to look it up online) that allows you to get on and off (they all stop at the Charlestown Navy Yard and you can see other sights as well but if you want to take the tour you should take one that allows you to get on and off) or you can walk to the dock in front of the New England Aquarium where you can then take a water taxi right to the Charlestown Navy Yard.
You should not be discouraged when moving around Boston. No matter what kind of transportation you decide on you can see a lot along the way and mid-Sept we usually have some of our best weather.
Hope this was helpful and let me know if you have any other questions.
Chelsea
