I’d say the most important part is moisture. When a desert starts getting more rainwater, it starts to be an interesting habitat for algea and cyanobacteria (all they need is sun and moisture). These organisms start colonizing the desert, because it’s not hostile for them anymore. As they live and die there, organic matter starts to pile up and allows other organisms that consume this matter to colonize the desert as well. Soil is slowly developing and allowing more and more plants and animals to inhabit the place. The whole proces is very slow. You can do the same (and faster) through artificial means, but you have to water the land and take the water from somewhere else. If you stop watering, the land turns into desert again if there’s not enough rainfall. At some places that are not dry naturally you could reestablish a long term green habitat - e.g. instead of a dam and dry land surrounding it, you could recreate a wetland forest with a meandering river, which would help the surrounding area, because forests create their own small water cycles so more rain can be expected around them.