Combine well-draining, quality potting soil and organic compost in a 3:1 ratio. Pour the growing medium into a large pot until three-fourths full. Tamp the medium with your hand to remove trapped air bubbles and help it set. Mist the potting medium lightly with water so it is easier to poke planting holes through it later.
Center the topiary frame over the potting medium and lower it. Lightly push the base of the frame into the medium to anchor it in place.
Immerse handfuls of sphagnum moss in a container filled with water and leave it for 20 minutes. The amount of moss stuffing you need to use depends on the size of the frame; use enough to fill the inside completely.
Lift a handful of moss from the container, drain excess water and insert it into the base of the frame, directly above the potting medium. Continue packing handfuls of moss into the frame until it is completely stuffed. Walk around the container and insert handfuls of moss into visible gaps you left in the frame.
Wind transparent twine of fishing wire around the frame to hold the moss stuffing in place and keep it from falling out. Wrap it along the contours of the frame so it defines its shape.
Insert a stick or your finger through the moss in the frame so it penetrates the potting medium below to form a planting hole for the plant. Apply some force when pushing through the moss, but work carefully to prevent it from sticking out thorough the frame or twine.
Lower the root ball of an ivy plant into the planting hole and cover its roots with soil before sliding your hand out through the frame. Repeat the process of forming planting holes throughout the topiary frame, spaced 5 to 6 inches apart, and plant ivy in each hole.
Spread the vines of the climbing ivy plants over the wires of the topiary frame to encourage them to spread and cover it completely. Attach the tendrils to the frame with bobby pins.
Water the topiary 1 to 2 times a week until the soil is evenly moist. Continue to attach growing tendrils of the climbing plants to the topiary frames to cover them completely.