Well, if what you want to do is grow food "for now", as opposed to creating an integrated system, then you can use raised or sunken beds and Ollas.
Ollas are used for water delivery by creating an unglazed terra cotta pot with a long, thin neck that is about 1 foot or shorter (longer for bigger pots, etc.. depends on your needs), and a bulbous jar beneath. There is usually a stone or glazed 'stopper' for the top. Sometimes there is a rain collector.
You bury the olla into the dirt with the top barely protruding, and it provides water for as far away from it as its radius. It is incredibly conservative in water usage.. essentially, it acts like a manmade aquifer, or maybe a tiny subsurface pond. Also, because of the nature of osmosis (which is how the water comes out of the pot and into the soil) you cannot overwater.
Doing ti this way means you can cover the soil over with something fairly water impermeable, either organic (mulch, etc) or not (plastic, greenhouse cloth, etc), and you have a closed, water conservative system that will work in almost any climate.
Here is just one of many references.
And yes.. if you are growing vegetables in the desert.. you should at least partially shade them!!! That is, unless you are growing varieties you know for sure will work in full sun, in your climate.
Ah! And here is a thread here on permies about them: