Summarize:

The best indication that a fig is fully ripe is when it falls to the ground. Rinse the figs with cool water to remove dirt and other debris, then pat them dry with a dishcloth or paper towel. Use a paring knife to cut the figs in half from stem to tip on a cutting board. Cutting the figs in half will help them dry more quickly. Put a layer of cheesecloth on top of any wooden or wire rack, such as those intended for cooling or dehydrating. In order to dry properly, the figs need airflow from above and below, so don't use a solid surface like a baking sheet. Place the figs cut-side up on the cheesecloth. Alternatively, you could put whole figs on wooden skewers and hang them in the sun, using clothespins to attach the skewers to branches or to a clothesline. This will protect them from insects as they dry. Tuck the cheesecloth tightly around the drying rack, securing it with tape if necessary, to make sure it won't come loose. If you hung up your figs instead, you won't be able to protect them with the cheesecloth. This method works best when it is very dry and hot outside. Don't place the figs in the shade, or they won't dry as quickly and may spoil before they're properly preserved. You'll need to bring them in each evening so they don't get spoiled by dew. Each morning, turn the figs over so they dry evenly on all sides and then place them back outside in the sunlight. The figs are ready when the outside feels leathery and no juice can be seen on the inside when squeezed. If the figs remain a little sticky, you can finish them in the oven. Tupperware or Ziploc bags are both options for storing your dried figs. They'll last several months in the fridge, or up to 3 years in the freezer.
Rinse fully ripe figs. Cut the figs in half. Lay them on a wire or wooden rack covered with cheesecloth. Cover the figs with cheesecloth. Place the rack in full sunlight during the day. Return the figs to the sun for 2 to 3 days. Store the dried figs in airtight containers in the fridge or freezer.