Good question. First of all it's worth mentioning that not all deserts are sandy. In fact, most are not and so frequently they are rather flat. Even in the Sahara only about 20% of it is made up of sand - most of it is in fact bare rock. read more
As for how fast they move, again it depends. Wind speed is the crucial factor here though. The dunes in the Great Sand Dune National Park in Colorado, USA, move around a metre each week thanks to fast wind speeds of about 65 km/h. read more
How fast a sand dune moves depends on a number of things. Of course, the speed of the wind is a big factor. Wind that is blowing 45 miles per hour will move more sand than at 17 miles per hour. The size of the dune is also important. Smaller dunes with less sand move much more quickly than large ones. The vegetation also plays an important role. read more