Select a planting site in full sun for a purple plum tree. Prepare the planting site with a loamy soil that may also contain some sand or clay. Add peat to the soil as needed to lower the soil pH to between 4.5 and 7.5. Loosen the soil at least to the depth of the purple plum tree's root ball.
Dig a hole with a shovel that is at least three times the diameter of the purple plum tree's root ball and at least as deep. Remove the tree from its nursery container and place it in the hole. Adjust the position of the tree so that it is at the same soil level as it was in the container.
Fill the hole with soil and firm it around the purple plum tree to hold it in place. Water the tree immediately after planting. Provide the tree with 1 to 2 inches of water per week during the first two growing seasons. A purple plum tree should not require supplemental watering after this point, unless the soil becomes completely dry.