It would be pretty hard for humans to create all the things necessary to create a true desert as Dale has mentioned, many things have to come together in order to form a desert.
The one thing humans do that does help desertification along is the removal of Old Growth Forest, that changes the climate in many ways.
We are very efficient at killing soil, but that doesn't make it a desert, that just makes it barren dirt.
Even this will be reclaimed by nature once humans are gone from the area.
There are deserts now that used to be covered with
trees, once the trees were cut down in clear cut method, the other variables that create deserts were able to do the rest.
One of the best examples would be Lebanon, they used to have great forests of cedar trees but in ancient times there was great demand for Lebanese cedar, now there are none and where the forests were, is desert
land.
Most deserts will have areas of Oasis, these can be considered natures greening of the desert.