A lot of people wish they knew the answer to your question. When people over-use land and it becomes desert, there's no fast, simple way to return that land to forest, grassland, or whatever else it was before.

It may seem like you could just toss seeds out and they would grow, but this is rarely successful. When there was vegetation, soil was shaded, and dead vegetation acted like a sponge and cover to hold water in the soil. Now, the soil is usually poor and dry, so the seeds don't sprout or take hold. Could we use artificial soil covers and water? Maybe, but it's a lot more expensive.

Without shade, new sprouts may not survive. If you look at a desert community you will often see lots of plants growing under a tree, but few plants growing outside of the tree's shade. This shows us how important shade is in the desert. Could we plant larger plants, water them, and provide shade? That may work, but it's going to cost a whole lot more.

Another wrinkle is that there may be other species, including plants,animals, bacteria, or fungi that influence the survival of the plant you're trying to grow. Do they need a certain animal to move their seeds or pollen? Has a non-native species moved in that produces disease, competes with it, or eats it?

You may be wondering how the original forest or grassland got its start if this process is so hard. One answer is that new growth may be able to fill in from the edges, but it takes a very long time. Another answer is that the climate may have been cooler and wetter back when the forest or grassland got started.

So it may be possible to reverse desertification in some areas, but only with a lot of time, money, and research.

No, there isn't a way to reverse the overall damage of desertification. If there is one particular problem of interest in one region, then temporary solutions and can be applied. Drying out land can cause increased air pollution from dust picked up by the wind. Spraying water on an offending dust field could limit the air pollution caused by it, but would also be a waste of water. Desertification could also ruin habitats for certain species. Again, moving water from one location to another could save one species, but could harm more where the water was taken from.

Desertification can be reversed but it takes a long time, how long depending on what is responsible for the desertification. That said, it's not really a single process:
desertification can result from climate change (i.e. less rainfall), from the loss of topsoil, or from the poisoning of the soil, especially by salt buildup. The Earth's climate is continually changing and always has been, but with our current understanding it is difficult to predict and even harder to control, so some areas are becoming deserts while others that are currently deserts are being invaded by trees and turning into forests. Topsoil builds up gradually over time as a result of geological processes that break down rocks as well as biological processes that result from vegetation growing on said soil. In order to restore topsoil, then plants must be allowed to grow on the depleted terrain for long enough for the topsoil to reform. This can take centuries or even millennia.

Finally, poisoning of the soil can be cleaned up by simply allowing a flood to occur - which won't, sadly, in many of our river systems that have been dammed, until, that is, the dams are removed.

Desertification, on the scale of a human-life, is irreversible. While there are a number of human factors that can contribute to desertification such as grazing, population, and development, ultimately the only way to reverse it would be to reverse the local climate and rainfall patterns. Humans do not currently have the technology to do this, and, I would argue, even if we did have the technology to affect local climate, we may not want to use it. Local climate patterns are intimately tied to global climate patterns and if we make it wetter in one location, we could inadvertently make it drier in another. The human factors that contribute to desertification are all caused by overpopulation. So the only long-term solution I see, and unfortunately not at all satisfying to the people currently subjected to desertification, is to reduce local and global populations. Improving the standard of living while simultaneously educating women about family planning has been successful in a number of countries to significantly reduce population growth rates (e.g. Mexico is a success story).