Having thought about how to make water in the desert, the next obvious question is what do with it all. Well, of course, there is no shortage of things you can with water, but the obvious thing would be to grow some plants.
Depending on the kind of soil, this processes could take quite a long time; in the Sahara, where the soil is very sandy, it retains little water, but most deserts do not have soil this poor; the desert areas of Australia or Western US can all support plant life.
With a supply of water, some kind of irrigation system could support a significant area; some kind of underground porous claypipe probably at a metre or more in depth would do the trick. Slowly fed with water, seeping out, this could cover quite a broad area in a fairly coarse fashion. Initially, it might just support local plants – cactus, grasses, that kind of thing.
Once harvested, there are lots that could be done with this material. Biogas production would be one that I have described before. But in addition, you could build some sort of raised bed – using cactus to form the edges of the bed, everything and anything else in the middle, and then layered over with digestate from the biogas production. This might allow cultivation of all sorts of crops, including sisal, agave and aloe, as well as some trees. Waste products from this would in their turn be biogasified with the leftovers returned to the land.
One of the interesting thing about trees, of course, is that they start to produce their own weather; rain forest is not forest because of the rain, but rain because of the forest. I don’t know how big an area of vegetation would be needed for this to happen; I guess it depends how fast the winds are. But at this point, the water produced in the desert would essentially be recycled; taken up by a plant, and then used again by another plant, till eventually, it would disappear down wind into uncultivated areas.