Deserts are really magical places and they're awesome for camping. Just like beach camping, deserts are a place where you have a little bit more to worry about than you normally would in the forest. With deserts, the biggest thing to keep in mind is that it may be really hot during the day, but it's going to be super cold at night. So although you may be thinking, I'm camping in New Mexico or California where it's warm during the day, you need to be prepared with thermal sweatshirts, sweatpants, socks at night.
Another things about deserts is that they're prone to flash flooding. The ground's really hard, there's a lot of ravines and dried up river banks. And when it rains, where you pitch your tent could end up completely flooding. So as you're looking for a spot to pitch your tent, you want to look for a place that is a little bit higher ground. Just try to assess out. If it looks like there was a river there before, don't pitch your tent near it. The other things about the desert is that the ground can be really hard, so this may be the trip to invest in a sleeping pad and give yourself a little bit of extra padding in your tent.