Plants that grow in deserts are called Xerophytes.

These plants have a long tap root system. Their roots reach deep inside the soil to absorb water from the lower parts. They have the capacity to store water for long periods of time.

Their stem is green and performs photosynthesis. The leaves are normally turned into thorns for protection of the plant. 

E.g. Cactus
They have long, fleshy roots so that it can go deep in the sand and store water /leaves are modified to thorns to reduce water loss / the stem does the process of photosynthesis as there is no leaves