Find a mold that suits your shape to bend the chicken wire around. This should be a firm, basic structure to bend your wire to. Don't use any items that can be popped or damaged by the sometimes sharp wire. Slow-growing and formal topiaries are grown with shrubs like yew, boxwood and holly. Many people create sphagnum moss topiaries which grow vines quickly.
Measure the object you are attempting to mold; take a measurement for each surface area you are fitting. Make sure this size coordinates with where you are locating it in your yard. Cut strips of chicken wire to fit each surface. Cut strips so you can build the frame in two pieces. The topiary frame needs to be created halves so it can open like a clam shell; this is for changing plants or other plant maintenance in the future.
Mold the chicken wire around the mold by warping the wire with your hands; wear gloves to protect your hands. Start with the bottom of the mold, turning it upside down. If you need to create an angle on the shape, like a cone or sphere, simply cut a triangular shape from the chicken wire; the width of the triangles base is how much you are decreasing one side's perimeter; reattach opens seams with garden twist ties. To create dramatic corner angles, bend the wire around a 90 angle and pinch the corner edge with pliers.
Create the top half of your topiary frame in the same way. Make sure the top half overlaps the bottom half of the frame by 1 or 2 inches. Attach the two halves with garden ties; if you need to re-enter in the future, you will have to replace the ties. Insert stakes through the bottom half that will support your frame.
Place your topiary over new growing shrubbery or wrap it in the sphagnum moss to begin growing vines on it. You can use hardier, low maintenance plants in the center that will be more difficult to tend; place more temperamental, decorative or flowery shrubs around the perimeter.