It depends on the type of animal. For herbivores, the diet of
camels, antelopes, jackrabbits, etc can includes grasses and
shrubs, while peccaries (wild pigs) eat tubers, and some birds and
rodents eat seeds.
Carnivores like cheetahs and mountain lions eat antelope or deer,
while carnivores like snakes, coyotes, large lizards, and birds of
prey eat small mammals and lizards. Animals like birds of prey and
coyotes eat snakes and large lizards too, and the road runner feeds
almost exclusively on rattlesnakes. Meerkats, some birds, and small
lizards usually eat insects.
As for insects, locusts (similar to grasshoppers) eat grasses.
There are butterflies, which drink nectar (a few bats also drink
nectar in the desert, but obviously they aren't insects). Scarabs,
or dung beetles, are relatively self explanatory when it comes to
their dietary preferences.
There may be a few exceptions, but that is the overall picture.