I acquired a leggy Desert King in a container. It has a few leaves right at the tip indicating life. How can I get it to branch out so I can get some figs?

Air-layer the top portion at 3' height from soil surface in the pot. By mid-June you may have two 3' tall plants. You may have to cut the top of the air-layered plant (about 6") for that plant to branch out too. Root the 6" cutting to get 3rd plant. Then you will have an orchard of 3 plants.

Since it has broken dormancy, saw if off where you want branches. After dormancy breaks, they seem to break more buds, rather than just the apical bud, when pruned. Root the cuttings.