Figs are pretty easy to propagate from cuttings. Here is some info from the
Fig Fruit Facts from the California Rare Fruit Growers (check out the Fruit
Facts on the site for many many other fruits too!), crfg.org.

"Propagation: Fig plants are usual propagated by cuttings. Select foot-long
pieces of dormant wood, less than 1 inch diameter, with two-year-old wood at
base. One-year twigs with a heel of two-year branch at the base may also be
used. Dip the cuttings in a rooting hormone and allow them to callus one week
in a moist place at 50-60° F. Summer cuttings may also be made, but they do
best if defoliated and winterized in a refrigeration for 2-3 weeks before
potting. Leafy shoots require a mist bed. Particularly rare cultivars may be
propagated on rootstocks, or older trees, topworked by whip, cleft or crown
grafting, or chip or patch budding. Rooted cuttings should be planted in 22 to
30 feet squares, depending upon the capacity of the soil and the ultimate size
of the tree. Keep roots moist until planted. Never transplant or disturb a
young tree while it is starting new growth in spring, as this is likely to to
kill it. Cut the tree back to 2 ft high upon planting and whitewash the trunk."