Occasionally a desert village will start a project that requires food. So far the only way I've found to get food is 1-3 at a time through the use of basic animals. How can I get a lot of food into my desert villages to finish these projects?
You've got the same two basic options as anywhere else: Domestic Animals and (Fruit) Plants.
In the desert, both Fruit Plant and Herb come out as a Withered Shrub (that only gives a little bit of natura). Luckily, the Ocean Giant starts with Growth Aspect, which will allow you to upgrade to Agave. Agave give 15 food if next to another plant, so two or more together should generate plenty of food early in the game.
Animals are also a pretty good option, even with low level giants. The basic Kangaroo Rat has 3 food and 2 range, so you can get 15 food too, but you need all those patches to be clear, within your town's borders and to include a mineral. On the other hand, you can put animals just outside your towns borders and still benefit from the range that is inside your borders, and aspect bonuses apply across the animal's whole range, so each +1 food from a Hunt or Herd aspect can generate up to +5 food for your towns.
You might also have access to the Salt mineral. It's only 5 food, but it gives gold and tech as well, and sometimes a little bit of every resource is just what you need.
Later on, leveling the Fruit (forest giant) or Herd (ocean giant) aspects can unlock more advanced food options in the desert too.
Note that mountains are a seperate Biome with different plants and animals, but the general rule of "Level Fruit and Herd aspects to get more food" applies there too.