In reference to the desert: I only have experience in a "high desert" environment (Nevada) but I imagine that the weather conditions aren't much different in NM during the summer months. Unless you have the experience, you should not be planning to walk through the desert alone. That is a very dangerous situation. Try to secure a ride or save up and take a bus to the next city. If you find yourself hiking though, here are some things to keep in mind.
SUN: Having something like a large umbrella is very important for keeping the sun off you. Light, Loose clothing is also important to avoid overheating, without having to strip off your clothing and risk getting sunburnt. A sunburn will dehydrate you very quickly. A wet rag around your neck is a good way to keep cool. A wide brim hat is a good item to have. You can also wear a cotton sheet, like a shemagh. Sunglasses to protect your eyes are important, especially if they are light.
- Hike at night. Rest in the shade during the day. This will greatly reduce your water loss, and keep you safe from sun exposure.
WIND & AIR: Even when not active, simply exposing your skin to dry air will dehydrate you. Wind will increase the speed in which this happens, so keep that in mind when you are deciding how much water to bring. Wind also kicks up dust, so having a bandana and sunglasses to protect your face is a good idea. If you have the resources, building a raised bed will help keep you cool because it will allow air to circulate under you. Sand can stay hot for quite some time after the sun goes down.
Water: Obviously, water is extremely important. If hiking and the temp is around 110, expect to consume about 2 gallons of water a day. You will also need a way to replenish body salts and electrolytes lost from sweat, so it's a good idea to carry lots of gatoraid powder mix, sport beans, gel, or something similar.
Insects & animals: Scorpions are common New mexico. They are nocturnal. Generally, the smaller the pincers, the more venomous it is. keep boots upside down and elevated on poles at night. They like dark holes, overhangs, and burrows, so avoid those during the day. Rattlesnakes is another thing to watch out for. They can be found in the morning sunning themselves on rocks, and in the day, in cool places like caves and rock overhangs. They also like to lay on asphalt during the evening because the road will radiate heat after the sun goes down. Coyotes are also common, but are less of a danger, as long as you don't leave food all around you. Try to eat at a different spot than you are sleeping.
Communication: Don't rely on a cell phone. Most remote areas don't have cell reception. Try to tell a friend or trusted individual your route, and when you expect to be in town. Once you get to your destination, call them so they know you made it. If they don't hear from you, they can assume that something went wrong and send a rescue party to search for you.
hope that helps.
