Some trees have extremely long taproots that stretch deep down into the underground water sources. These plants do not have to rely on regular rainfall because they have another kind of water source.
Most of the other desert plants, eg. the creosote bush, however, have a big mass network of shallow roots near the surface of the ground. The roots absorb every drop of rain they can when there is rainfall. They are shallow, specially designed for absorbing the water as soon as it reaches the ground. The shallow roots extract every available drop of moisture on their patch of the desert.
Some desert plants have thick roots, bulbs or tubers underground to store food and water. The bulb can be swollen with water. The part of the plant that is exposed to the surface may look dead, but actually it is very much alive. When it rains, these plants spring to life, blooming with leaves, flowers and fruit.
Another kind of desert plant also stores water, not underground, but in their trunks, eg. the kokerboom tree. The trunk of this type of plant is swollen with water. These plants can live for a long time without rain because they have their own water supply.