Dividing perennials is an easy way to gain more plants, for your garden or to share with friends, and to make space for other plants. More importantly, it is beneficial to the health of the plants; increasing healthy air flow and lessening flopping stems by reducing crowding and also spurring more vigorous blooming.
Autumn is an especially good time for dividing perennials due to the generally cooler temps and more reliable moisture reducing the stress of being disturbed from their comfy garden spots. Autumn is also when perennials focus on root growth more than top growth, so they will quickly “take hold" again when replanted after division. Dividing can be done at other times of the year, but a bit more attention to after-care will be needed, especially if done during hot, dry spells.
A shovel is handy not only for digging up perennials, but also for the actual task of dividing - a garden knife or hand saw may be needed for denser root clusters. If the divisions will be transplanted back into your own gardens a tarp, buckets, or a wheelbarrow are handy for holding them as you get their new holes dug. Empty pots come in handy if you'd like to share any divisions with others.
Dig up each perennial to be divided at a width defined by the outer edge of the plant's circumference and a depth of 6-12" – as best accommodates the majority of roots. Lay the plant on its side and slice through the root mass completely with your tool of choice. For each division from the original chunk to be replanted, aim to have a good section of both top growth and roots. Any plant divisions with very few roots, such as from plant centers that had grown sparse with age, are best left to the compost pile. Keep the divisions shaded while preparing their new planting holes.
Planting holes dug for your divisions should be sized to allow for the roots to be fully extended, not bent or circling, and for the crown (where stem meets roots) to be at soil level. This may mean creating a soil mound in the center of the hole for the crown to sit atop while the roots drape downward. Backfill the hole with soil, tamping gently to remove excess air pockets, then water thoroughly. Transplanted divisions may initially need more frequent watering until they establish themselves in the garden, so check them regularly during the first weeks after transplanting.