Figs dry nicely. First, though, you must let them ripen fully to develop their flavor. And the only way to know that they’re fully mature is to let them drop from the tree. Harvest them quickly, wash and dry them, and cut them in half. Place them on a drying surface, skin-side down. (The drying surface may be the rack from a dehydrator, cooling racks that you intend to put in the oven, a clean screen or wooden frame with a clean, old sheet stapled to it for drying the figs in the sun, etc.)
If you plan to dry them in the sun, you need warm days with little humidity. A warm, dry breeze circulating around the figs for two days is ideal. Bring your trays in before the evening dew. To discourage bugs, you can prop a layer of cheesecloth up across the trays.
You can also dry the figs in the oven, but you want a temperature no higher than 140°F (60°C). And 115° to 120° (45°C to 50°C) is actually best for fruit. Many ovens cannot be set that low, however, so you may need to find some absolutely safe way to prop the oven door open a little to allow the excess heat to vent. Some people let you go as high as 160°F (70°C), but at that temperature the fruit may actually begin to cook, which is not your goal. Or the surface will dry out before the interior, trapping moisture inside, and leading to the development of mold. At a temperature around 120°, the figs will take between 8 and 12 hours to dry. If you use a dehydrator, follow the manufacturers’ instructions.
After the figs are dry and leathery, you should “pasteurize” them to kill any insects that may be lurking in the cracks and crevices. You can either heat them in the oven for 10 to 15 minutes at 175°F (80°C) or put them in freezer bags and freeze them for at least four days. (The freezer method is a little less destructive to vitamins, minerals and texture). Afterwards, if you keep them in the refrigerator, they’ll last for 18 to 24 months. In the freezer, they’ll last for 5 to 8 years.
Which ever you choose, remember to keep eating those figs — you'll have another crop next year!