Water. Plan all hikes with at least a 1/3 reserve of more that you think you'll need.
Springs/creeks are unreliable and you need a reserve just in case. Plan on carrying ALL your water, and don't push your luck. Depending on the weather, dress light and loose. I wear an old long sleeve, white, floppy, cotton poly blend dress shirt and a wide brimmed hat. I like convertible pants...light material. Umbrellas are wonderful portable shade...make yourself a ultralight umbrella. I like trail runners instead of boots, don't kick a horse crippler (armour piercing cactus).
Plan your equipment to handle wide temperature swings, but keep it as light weight as possible. Crazy hot in daylight, cool/cold at night, with dry high winds in between.
Never had a problem with food storage in the desert. It stays in the pack, near me unless I know of critters in the area. In the mountains, there are usually trees to hang from. Many national parks now have bear boxes for storage in each campsite. If you are going to a park, by all means pick the brain of the desk ranger.
Oh, and plan on returning over and over again....deserts are wonderful!