I bought a Brown Turkey Fig tree on clearance for $7 a few years back and now have about 30
trees. It is the easiest thing I have propagated by cuttings. I cut off pieces, stick them in sand (my
native soil at the beach), and keep them moist and in the shade. It is a good idea to remove most/all of the leaves, otherwise they will fall off on their own and possibly suck the life out of the branch in the process. I have done it with cuttings 3" long to 3' long and had few failures. My only issue has been an occasional white grub attack on trees in larger containers or after planting them in the ground.
I agree that it would make sense to find a donor tree to take a cutting from if you can find one. Otherwise you can check out the clearance racks at the big box stores or perhaps become friendly with a
local nursery that has figs and maybe score one for cheap/free that has been damaged or similar. One tree I planted was about 3' tall when white grubs ate the roots and I managed to pot it up, take the leaves off, and get it to grow again! They are really tough trees! Some things wouldn't be worth it to try and save if it is root bound or severely damaged, but a fig would be one of the easiest to save from a disaster.