You don't need the extra-heavy boots mountain climbers wear, but you need sturdy boots with at least ankle height. Running or cross-training shoes might suffice for easier trips, but anything long and rough calls for sturdier boots, even more so than forested hiking areas in northern mountain ranges. To enjoy desert hiking even more, take advantage of the early morning or late evening. The desert light is the purest early and late in the day, and usually the temperature drops to a more tolerable level. Plus, you stand a better chance of seeing desert wildlife.
Most desert fauna is nocturnal, and even diurnal species usually remain inactive during the mid-day.
Dig around in the closet for something dull. Your wilderness partners will appreciate it. Try out the clothing before leaving home to make sure everything fits loosely with no chafing. In particular, make sure your boots are broken in, lest they break you on the first day of the hike. For day hiking, bring high-energy snacks such as raisins or granola bars for lunching along the way.