Plan your animal topiary, estimating its general height, width and length. Plant the juvenile shrubs in a suitable area for display and enjoyment -- using enough shrubs to easily fill in the topiary as they develop.
Place your topiary frame over an existing evergreen shrub or series of shrubs, as an alternative, and cut it down to fit the frame's contours. Holly and other vigorous evergreens that tolerate major pruning are best for this approach.
Begin pruning and training when young shrubs are suitably sized -- at least somewhat larger than the frame. Trim a few inches on any stem per session, using hand shears. Head back the stem to just beyond a healthy bud, so new leaves will neatly cover the cut.
Prune 1 inch off areas you'd like to fill in with more or thicker vegetation, because even minimal pruning will stimulate bushy new growth. Cut no more than 3 inches on stems that require major cutting-back. Cutting too much too fast risks killing crucial branches.
Thin any stems that won't fit within the topiary frame -- or stems surrounding the shape if you're cutting into an established hedge and need to make your animal stand out -- by cutting them back all the way to the ground.
Repeat this clipping and training process every three months during periods of active growth, gradually perfecting the form. You can use hedge shears for quick finishing cuts, once the final form has been achieved, but always clip close to healthy buds.
Leave the topiary form in place if desired and use it as a permanent guide for maintenance pruning. You can also remove it between training and maintenance sessions, putting it back in place to guide pruning cuts as needed.