I am not sure about which do you ask?
A. the situation of how desert has been spreaded OR
B. why does desert spread around the world and by what means
If you want A, then the picture provided by the above user is clear enough
but in case you want B, here is my answer:
Desertification is the degradation of land in arid, semi arid and dry sub-humid areas resulting from various factors including climatic variations, but primarily human activities. Modern desertification usually arises from the demands of increased populations that settle on the land in order to grow crops and graze animals.
Deserts may be separated sharply from surrounding, less arid areas by mountains and other contrasting landforms that reflect basic structural differences in the terrain. In other areas, desert fringes form a gradual transition from a dry to a more humid environment, making it more difficult to define the desert border. These transition zones have very fragile, delicately balanced ecosystems. Desert fringes often are a mosaic of microclimates. Small hollows support vegetation that picks up heat from the hot winds and protects the land from the prevailing winds. After rainfall the vegetated areas are distinctly cooler than the surroundings.
In these marginal areas human activity may stress the ecosystem beyond its tolerance limit, resulting in degradation of the land. By pounding the soil with their hooves, livestock compact the substrate, increase the proportion of fine material, and reduce the percolation rate of the soil, thus encouraging erosion by wind and water. Grazing and the collection of firewood reduce or eliminate plants that help to bind the soil.
In large desert areas, sand dunes can encroach on human habitats. Sand dunes move through a few different means, all of them helped along by wind. One way that dunes can move is through saltation, where sand particles skip along the ground like a rock thrown across a pond might skip across the water's surface. When these skipping particles land, they may knock into other particles and cause them to skip as well. With slightly stronger winds, particles collide in mid-air, causing sheet flows. In a major dust storm, dunes may move tens of meters through such sheet flows. And like snow, sand avalanches, falling down the steep slopes of the dunes that face away from the winds, also moving the dunes forward.
It is a common misconception that droughts cause desertification. Droughts are common in arid and semiarid lands. Well-managed lands can recover from drought when the rains return. Continued land abuse during droughts, however, increases land degradation. Increased population and livestock pressure on marginal lands has accelerated desertification. In some areas, nomads moving to less arid areas disrupt the local ecosystem and increase the rate of erosion of the land. Nomads are trying to escape the desert, but because of their land-use practices, they are bringing the desert with them.
Some arid and semi-arid lands can support crops, but additional pressure from greater populations or decreases in rainfall can lead to the few plants present disappearing. The soil becomes exposed to wind, causing soil particles to be deposited elsewhere. The top layer becomes eroded. With the removal of shade, rates of evaporation increase and salts become drawn up to the surface. This is salinisation, and inhibits plant growth. The loss of plants causes less moisture to be retained in the area, which may change the climate pattern leading to lower rainfall.
Hope this can solve you problem enough ^^