Choose a space within your desert garden that receives at least 70 percent sun. These plants can withstand midday shade, but enjoy high sun levels. The plants vary in size from 1 to 3 feet high by 2 to 3 feet wide, so leave enough space in the garden for a mature crown of thorns.
Dig a hole in your desert garden twice the size of your Euphorbia's root ball. If you are creating a desert garden from scratch, combine crushed rock and sandy soil in a 1-to-1 ratio. Build up a raised bed of at least 12 inches of this rocky mix, to create a soil suitable for desert gardening. Once you have the rocky base, dig the hole for your Euphorbia.
Slip on thick gardening gloves to protect your hands from this plant's milky sap, which can sting.
Lift the Euphorbia from its container and place it in the prepared hole so the roots spread out against the soil and the plant sits at the same depth as it did in the container. Push the desert garden soil around the roots to complete planting.
Water the soil at the base of the plant until it becomes moist. Thereafter, allow the top inch of soil to dry out thoroughly before watering your crown of thorns, then water to moisten the soil. Do not give this plant too much water, since that will harm the roots.
Fertilize this plant in the late spring and early autumn using a slow release fertilizer. Apply the right dose for your size plant by sprinkling dry fertilizer on the soil around the base of the Euphorbia and watering to disperse nutrients.
Watch out for insect pests in your desert garden, which can include scale, mealybugs and spider mites. You may see insect pests with your eyes or notice evidence like webs from spider mites. Treat these with an insecticidal soap safe for use with cactus plants.
Prune the Euphorbia after two to three years of growth by removing dead or tangled stems. Wear pruning gloves when handling this plant and cut off the growth with lopping shears.