+1 to Sheeple Hunter and Leaftye's recommendations.
Some additional suggestions are:
* Learn about the area you live in and the area you intend to hike in. New Mexico is different from Arizona & California. Heck, Arizona has different conditions depending on where you're at. If you're in the high desert or mountain areas you can get chilled at night. In the southern low desert you're usually only going to run into cold nights in the winter time. It can get 115+ in the daytime but nights usually don't go below 85-90 (F), but the temperature difference can still cause a chill.
* Finding water and wild edibles depends on the time of year, and if you're in the southern desert in the summer, before the monsoons, you're going to have problems.
* The survival manuals often say & show graphics about using a barrel cactus to get water. It's absolutely bogus and will more likely make you sick and vomit up whatever water you had in your system.
* In temperate climates cotton kills, but in the desert heat it's beneficial. Add a loose fitting long sleeved cotton shirt to protect you from the sun and hold in body moisture. There's a reason Middle Eastern nomads use those robes - it's to prevent dehydration and severe sunburn.
* A wide brimmed hat to shade your eyes, forehead and neck. The standard boonie hat has a relatively narrow brim, but they're nice in that they roll up easy. Get the one with the wider brim.
* Carry a bandana or some type of cloth to help pre-filter the sediment & floating junk out of the water before you boil it.
* As mentioned by others, salt licks are commonly found all over for the open range grazing cattle. Another thing commonly found is cattle tanks full of water. There are bugs of all kinds in there, but water is water. Filter it before you drink, but if you're severely dehydrated, just drink. If drinking dirty water can keep you alive to reach safety, the effects from the microbes can be taken care of when you're safe and in the hospital. If it's a post-SHTF situation though, be sure to have something to purify your water with.
* Take extra water. Water is more important than food or that extra four mags of ammo. If you're low on water, don't eat as digestion uses up your body fluids.
We're out for days to weeks at a time either on foot, horseback, or dirt bikes. It's easy to find yourself in a survival situation in the desert, so learn as much as you can about your area and I'd even suggest some desert specific training.
Cody Lundin is based in AZ and his survival courses cover most of the desert southwest.
http://www.codylundin.com/
Another good instructor is Mark Wienert at LifeSong:
http://www.lifesongadventures.com/
Mark's school teaches mostly wilderness survival, but he does do a few desert courses in the southwest each year. He's very good and he & his wife Celeste are good & friendly people.
I've done some courses from Mark & Cody and can vouch for both of them as good instructors.
-Tig