The best way to get started with designing a desert-inspired yard is to study and emulate the natural world of the desert in all its beauty and variety. Even urban areas in the Southwest have reserved parks or buffer zones where the desert was left pristine. Walk or drive through these and observe the variety of plants--their colors, shapes and textures. A trip to a desert botanical garden is another way to get ideas.
If you live in the Southwestern deserts, there are many plants native to that area and to Mexico. Using these adds authenticity to your desert landscape versus choosing plants from tropical regions just because they can tolerate many days of sunshine each year. Plants that have survived the harsh desert conditions are most likely to be low water-usage plants. They are also adapted to the soil conditions of the arid regions of the United States. The soil you have on your property may lack nutrients and may not have proper drainage for certain kinds of non-native plants to succeed. You either have to make improvements to the soil or go with the plants designed to survive there.
You can bring almost any color into your yard with desert landscaping. Mixing plants that bloom in different colors, or have different-colored foliage, allows you to create a color palette with numerous possible combinations. First you have to learn what color bloom each plant has, and then sketch out a design mixing the colors for maximum visual interest when the desert plants flower each spring.
Concerns about water conservation in the arid regions of the United States have brought about a trend of xeriscape landscaping, using plants that require at most very small amounts of irrigation. In the heat and drought of mid-summer, many low water usage plants need at least drip irrigation applied every two weeks. Installing an irrigation system allows you incorporate plants that require almost no water beyond what nature provides with those, such as trees, that need periodic watering for healthy growth.
Homeowners are often reluctant to plant cacti and other desert plants because of the spines or thorns they have. Children and pets running through a path surrounded by thorny plants can be an accident waiting to happen. Place spiny plants in the back of the garden, and then edge the path with non-thorny varieties of flowers and shrubs to keep kids and pets at least 3 feet from the cacti. You could also group all the spiny plants together in the yard and put wrought iron fencing around them, so their beauty can still be enjoyed but no one will get close enough to the thorns to be hurt.