Are there any ways to stop desertification or to slow it down?

Desertification is a process that affects dryland ecosystems in every continent of the world except Antarctica. Most forms of desertification in the past century have been anthropogenic, or caused by human activity. Humans, therefore, can slow, prevent or reverse the process, something that is the goal of the United Nations Convention to Combat Desertification (UNCCD). 

One cause of desertification is overgrazing. This can be due to overgrazing of sheep and cattle or of predator eradication programs...

Desertification is a process that affects dryland ecosystems in every continent of the world except Antarctica. Most forms of desertification in the past century have been anthropogenic, or caused by human activity. Humans, therefore, can slow, prevent or reverse the process, something that is the goal of the United Nations Convention to Combat Desertification (UNCCD). 

One cause of desertification is overgrazing. This can be due to overgrazing of sheep and cattle or of predator eradication programs to benefit ranchers which lead to overpopulation of deer. In this case, most of the way to stop or to slow desertification is to stop allowing grazing on public lands and compel ranchers to pay fair market value for access to water. Riparian habitats are especially sensitive. If they keep their natural plant cover, they can keep arid lands green and productive, but when trampled by cattle and sheep, they turn into dry washes, and rain water becomes flash foods rather than a year round stream. Unfortunately the "welfare cowboys" of the west are a potent political pressure group and enjoy having their livestock operations subsidized by other taxpayers; your personal ability to change this dynamic is your vote. It is possible to restore the desert through holistic management, including managed livestock grazing and planting, but this will only be effective if overgrazing is stopped.

Another major cause of desertification is intense farming. Irrigation can deplete in-stream flows in rivers, degrading the moisture absorbing vegetation of the banks. Also, irrigation and fertilizers increase the alkalinity of the soil, and thus intensive agriculture in drylands leads to desertification. Again, this is a political issue, with farmers in areas such as the California interior able to draw water at below market costs and using irrigation to make short-term profits at the expense of desertifying vast swathes of farmland. It is possible to use crop rotation and and other sustainable types of agriculture to restore desertified farmland.

The book  describes the desertification of the American West in some detail.