Joshua trees only occur naturally in the Mojave Desert. If you live in or near there you can collect seeds during the fall when the seed pods begin to fall off the trees. If you don’t, you may not be able to find the seeds at your local nursery, but you are certain to find them online. They even sell Joshua tree seeds on Amazon.
Once you have your seeds you’ll need to germinate them. This gives them a much higher chance of growing once planted in the ground. You will first need some newspaper. Cut the newspaper on the fold to separate it into pages. Then cut the pages in half horizontally. Fold a piece of newspaper in half horizontally and wrap it around a can (soup can size works best). The folded side of the newspaper should be at the top of the can and the bottom of the newspaper extended past the bottom. Tape the side of the newspaper with a small piece of tape then wrap the bottom of the newspaper around the bottom of the can, securing that with a small piece of tape as well. Once the newspaper is taped you can remove the can. Its only purpose was to shape the newspaper. It is recommended to write the seed type and the date of planting on the newspaper. Fill your cans with soil, but leave about 2 inches between the soil’s surface and the top of the can. Set one seed on the soil in the can and then sprinkle with about 1/8 to ¼ inch soil on top. Your container should be set in an inch of water in direct sunlight. Temperatures above 60 degrees Fahrenheit are best. Seeds should germinate and sprout in 2 to 3 weeks. Once they sprout, take them out of the water returning them about every two days to water again.
Your newly germinated seedlings will look like blades of grass. Once the seedling grows to 1 ¼ inches tall it should be transplanted. It is recommended to make a tall pot to transplant the seedlings in. A tall pot is easily made out of PVC pipe. Simply get PVC pipe that is 6 inches in diameter and cut a section between 12 and 30 inches long for each seedling. Use duct tape to attach a small piece of window screen to the bottom. If possible, fill the tall pot with native, well drained soil. If not possible mix two parts washed sand, two parts perlite, one part humus and some long lasting Osmocote fertilizer. Then rip off the bottom of the paper pot and plant the entire thing into the tall pot.
Joshua trees can be transplanted into the ground when the are 6 to 10 inches tall. Keep in mind that Joshua trees take at least 10 years to reach 5 feet tall. Also, Joshua trees grow best in the Mojave Desert. The success rate of growing them in other areas is unknown. Let your tree have plenty of sun and it should do well enough.