Get a look at your friend's fig tree. If you get one it will likely eventually get as large as his. Also, you should ask him(her?) is it requires any special attention (especially in winter). If the "mother" tree is large it might have enough hardiness to sirvive winters unprotected, something a much smaller tree of the same kind might not be able to do.

Figs are generally propogated by rooted cuttings (though if he has a shoot coming up from below ground, it could have a somewhat developed root system already and would be a good way to start a plant of your own).

Figs like warm-sunny locations, especially when ripening fruit.

~Chills

raisemybeds, Many fig obsessions (mine included) started with the quest for "a" fig that will produce in a person's location. Many fig trees later, you are lucky if you have that "one" fig. That a friend has a fig that produces in your area, and is willing to give you a piece, is a gift of great worth.
All figs are not the same; they can vary greatly in their requirements. New England not only doesn't have the late season heat (which Chills mentioned is needed for ripening), it also has a short season. So finding a suitable fig is not easy. This fig apparently will ripen fruit under these conditions - wow.
You'd think that since figs have been around so long, that we'd know all of them. Not so. Many have been handed down, and not widely grown. These figs can be lost so easily. The owner dies and his "special" fig is lost. And believe me, a fig that fruits in New England is a special fig, whether it is a commercial variety or a family gem.
Figs do not need fertile soil to thrive. In fact in Europe they are given the "poorer" sites. It is said that better tasting figs and a hardier plant are the result of poor soil. On the other hand many folks on the Forum lavish love on their figs in the form of manure and swear by it.
If the fig in question needs to be winter protected (as Chills said, a question for your friend) another option might be to put it a pot. I keep many of my potted figs, unprotected, in an unheated garage over the winter. This will also give you the option of putting the fig in an area that is unavailable to an in-ground plant (driveway, patio, etc.).
I hope you will decide to take the fig (wonderful fruit) and let us know how it is going.

The key is to make sure it gets enough sun, especially if there are some big trees around you. The sun is nearly as high as it'll get right now and a spot that gets plenty of sun now might get only a fraction of that when figs are trying to ripen.

Thank you for all the good "food for thought". I am beginning to think I should take this tree, but I am now going to go over there soon and take a better look and ask the intelligent "fig" questions. I have a full sun area where I grow the strawberries, and was going to expand it (eliminate the lawn growing around it) to be a fruit growing area. I want to do this, including planting the fig tree, closer to the Fall season. Is that advisable? Is there an optimal time to do fig transplants? Shall I build a raised bed for it (as I have for everything else I grow)? My soil is high in clay, so I find raised beds to be indispensable. Thanks again for all your input everyone.

Just trying to bump this thread up to get an answer to my next query. When is the best time of year for me to get a "clump" of this tree and transplant it?

Before it leafs out - or after it drops its leaves. When it's dormant.
Personally, I don't think a little green showing would be a problem. And if you give it much TLC you could probably get away with doing it in leaf. It would probably shock, loose leaves and look terrible but they are tough; especially with a good root system.
In any case, I'd cut it back to balance roots and top. And I'm a great believer in seaweed emulsion for helping with any kind of plant stress.
Others might have a different opinion.

Take it. Like fignut said, if it's growing in your area it's special, an should be propagated as widely as possible. In fact, if you transplant it this fall when it's dormant you should get a bunch of cuttings as well, and offer them here. I'm sure you'd get a lot of takers; I'd like some myself.

I would gladly take a cutting even now. If you have any to spare let me know - I too am in Southern CT

especially if it's a tree that's does well in our zone without wrapping