Dig a small trench around the perimeter of your palm tree with your shovel. Do not make the perimeter too tight, as you will be trying to dig under the roots of the tree.
Dig under the tree's root system. You will need a small crew of lifters to help secure the tree while you are digging under it. Keep in mind that you can cut some of the roots in the root system if you need to. Measure the depth of the hole you dug after the tree is removed.
Load the tree into the back of your truck, and secure it to the truck using high-strength rope. The best way to do this is to run the rope around the tree multiple times and tie the rope to a secure location in each corner of your truck bed. Make sure the tree is tied in such a way that it moves as little as possible while the truck is moving.
Dig a hole in the new location that is slightly less deep than the tree's original hole. Place the tree in the hole (with assistance from your crew) and fill 90 percent of the hole with water. After the dirt has absorbed the water, add the soil to the hole and stomp it in thoroughly.
Fertilize the tree after you notice it is growing in its new spot. Do not fertilize the tree before then.