Examine the ivy topiary. Most topiaries come pre-formed to a shape, but if yours does not, you will need to determine what shape you want. Note any tendrils of the ivy that are growing at odds with the current or planned shape. These will need to be pruned away.
Train the loose ivy leaves to grow over the shape that you want them to turn into. This can be done by loosening the tendrils with your fingers and draping them over the part of the topiary where you want them to grow. You can tie the tendrils down with string if they don't stay on their own.
Prune any stray tendrils that are growing out of place. The ivy should be kept close to the base of the topiary and should not dangle anywhere. Cut the ivy back where it has grown too tall for the structure of the topiary shape.
Watch the ivy as it grows. Although the ivy is growing on a specific shape, every tendril should be able to receive sunlight. Ivy topiaries have a tendency to become too dense for the sunlight to reach the innermost pieces. The outer pieces should be trimmed so that the inner ivy tendrils can receive sunlight.
Remove ivy tendrils to promote further growth. When an ivy tendril is pruned, two will usually grow back where the original was growing. Use this technique to fill in any sparse patches on the topiaries.
Examine the topiary from a distance. If there are any stray leaves or twigs sticking out from the topiary they should be removed. This can be done by hand or with gardening shears.