[Adapted from Successful Perennial Gardening by Lewis and Nancy Hill]
Division is a simple form of pruning. It is as essential to good perennial gardening as the pruning of a fruit tree is to a productive orchard.
Propagate shallow-rooted perennials by gently pulling apart the clump.
Keep clumping plants healthy by occasionally cutting away sections of the exterior and replanting them elsewhere.
Bulbs can be propagated by separating and replanting them, or by removing the bulblets and setting them out in a transplant bed.
When plants have carrot-like roots, it is necessary to dig up the entire plant and use a knife to cut it into a number of smaller plants.