Select plants -- including trees and shrubs -- native to the desert. They will grow better, require less water and be easier to care for than non-native plants. Plants that may be native in your desert climate include yellow spiny daisies (Machaeranthera gracilis), prickly bear cacti (Opuntia spp), desert ironwood trees (Olneya tesota) and soaptree yuccas (Yucca elata), to name a few.
Plan out curved lines for the garden, which are generally more interesting than straight lines. A slightly curved walkway with pavers also looks nice.
Lay out your garden. Intermix green plants with colorful ones. Plant tall plants in the back and shorter ones in the front, or mix it up a bit. Grow similar plants in groups of odd numbers and stagger groups so ones that bloom in the spring are near ones that bloom in the fall and winter.
Plant a warm season grass, such as Bermuda grass, but note that you will have to irrigate it every couple of days, especially during the summer, to keep it green. As an alternative to grass, use rocks that are common in desert landscapes. Lighter colored rocks reflect sunlight more than darker rocks.
Lay 3 or 4 inches of mulch to conserve water. Rocks work well, but adding organic matter, such as compost, will add valuable nutrients to the desert soil. Note that organic matter needs to be replaced as it decomposes.