To keep your perennial gardens healthy you need to divide several kinds of perennials periodically. You know when yours need to be divided because the plants are growing in ever-denser clumps and the flower show isn’t as prolific as it was in previous years. The interior of the clump, in particular, may become disappointingly unproductive.
Good timing is important to give the divided plants the best chance of prospering. Early spring is usual, but you can divide some (notably poppies and peonies) in the fall.
Dig up the clump, taking care to get as much of the roots as possible without damage.
Most roots are in the top 12 inches of soil, and the root’s mass will usually be the diameter the plant plus 3 to 6 inches beyond the plant. For digging and transplanting, going larger than this shouldn’t be necessary.
Use a sharp spade to cut or cleanly break the clump into two or more pieces (divisions), each with an obvious growing point and some roots.
Work on the clump quickly so the plant parts don’t dry out too much (you can cover them with a tarp or mist them occasionally if need be). Discard any unproductive portions and any shriveled or rotten parts. Leave the roots surrounded with the soil to protect the root hairs from drying out and becoming damaged.
You can pry apart fibrous-rooted perennials with your bare hands; all others require sharp, strong, clean tools that are equal to the job: a stout knife, a trowel, even two spades or gardening forks braced back-to-back.
Replant the new pieces.
Plant some in the same spot and the others perhaps elsewhere in your yard (or share them other gardeners).
Water the divisions well, and look in on them regularly. They should generate new, smaller, vigorous plants.
Plant in good (fertile and well-drained) ground. Perhaps the original spot could use a dose of organic matter before you return pieces to it; when planting elsewhere in your yard, prepare a bed in advance so you can move quickly.