Create a soil mix for the olive topiary by placing equal parts of bagged potting soil and compost into a large bucket. Mix the two ingredients until completely combined.
Locate a plant pot for your olive topiary that is only one size larger than the nursery pot and has drainage holes. Fill the pot one-third to half full with the prepared soil mixture.
Remove the olive topiary from its nursery pot and center the roots in the pot. Add additional soil mixture until you reach the top of the soil ball.
Water the soil well after planting until all of it is moist. Afterward, water only when you can dig down 1 inch in the soil and it is dry.
Locate a window on the south or west side of your home and examine it over the course of 24 hours to ensure that it receives sunlight for at least six hours. Place the olive topiary pot directly next to the bright window in full sunlight. Keep the pot away from heating or air vents, which can cause it to decline.
Apply seaweed fertilizer to the olive tree topiary twice per month from May through September. Dilute the seaweed fertilizer with water as instructed by the manufacturer and pour it evenly around the soil in the pot. In the fall, switch to a granular 20-20-20 fertilizer and apply it once per month through the winter.
Wait until the late spring when new growth is beginning to appear on the olive stems. Prune off 1/2 to 1 inch from all of the branches of the olive topiary using hand pruners. As you prune, follow along the natural designs of the topiary, such as a globe, to refine the shape. Also make all cuts at the intersection of another branch.