Dig them up, chop into pieces, and replant. By dividing your perennials, you'll not only get more (free) plants, but — harsh as the process sounds — your perennials will actually appreciate it. In fact, most perennials grow best when divided every three to five years. You'll know your perennials are ready for dividing when flower size diminishes and the center of the plant becomes brown and dead.
The day before you plan to divide plants, water the soil around them, making sure the entire root zone is moist. Next, prune the tops of the plants, leaving 6-inch stems. Removing foliage reduces moisture loss and helps minimize transplant shock. If you'll be planting the divisions in a new garden bed, prepare the soil by loosening it with a garden fork and amending it with compost.
If possible, choose a cool, cloudy — or even misty — day for dividing plants. For most plants, it's critical that the roots don't dry out so have a hose or bucket of warm water nearby.
Starting about 6 inches from the stems, use a shovel to dig down deep around the circumference of the plant, trying to get as much of the rootball as possible. Continue loosening the plant until it can be lifted from the soil. If the plant is too large to remove all at once, cut right through the plant and lift it out in clumps.
The root mass can be separated according to the type of root structure it has. If the roots are matted and have no apparent pattern, this indicates a spreading root system. Plants such as bee balm, coneflowers, asters, and lamb's ears have spreading roots. Try to pull the roots apart by hand. If they're too interwoven try this method: Place garden forks into the center of the plant so they're back-to-back in the rootball. Use leverage to pry the roots apart. If the plant is large, repeat the process to divide the root mass into quarters.
Clumping root systems have thick, fleshy, roots with multiple growing points. Examples include hostas, astilbes, and daylilies. Cut the root masses of these plants with a knife, or try the garden fork method described above.
I must admit I often simply dig up plants and slice the rootball into pieces with a shovel, and the plants do just fine.
Keep the divisions in a shady spot and moisten as necessary to keep roots from drying out. Plan to get them in the ground right away. If you must wait a few hours, wrap the roots in moist newspaper. Set the divisions in the ground at the same depth as they were originally planted.
Irises have rhizomes, which are horizontal swollen stems sitting just below the surface of the soil. To divide irises, start by cutting the foliage back to about 6 inches. Dig up the entire plant and shake off the soil so you can see the roots. Begin separating the rhizomes by pulling or cutting them apart. Discard large rhizomes that have no leaves attached. Examine the remaining rhizomes carefully. If you see holes or a rhizome has any soft, mushy spots, it's probably been attacked by borers so discard it. The ideal rhizomes for replanting are about as thick as your thumb and sport one or two leaf fans. Set these in the soil so that the rhizome is at or slightly above the soil surface.
Tuberous roots, such as those of dahlias, can be cut apart with a sharp knife. Make sure each piece has a section of the original stem and at least one bud. Plant tubers 6 inches deep in loose, well-drained soil. In USDA Hardiness Zones 8 and warmer, dahlias will overwinter, especially if soil is well drained and the bed is mulched with straw. In colder climates, store the tubers in a cool, dark place over the winter and replant in spring.
After planting, firm the soil around roots to eliminate air pockets and water the plants thoroughly. Once soil has frozen in fall, mulch the plants with an organic mulch, such as bark chips or straw, to prevent alternate freeze-thaw cycles that can heave plants out of the ground.
Some plants don't need to be divided and may not recover if they are dug up and their roots are damaged. Examples are butterfly weed (Asclepias), euphorbias, oriental poppies, baby's breath (Gypsophila), gas plant (Dictamnus albus), Japanese anemones, false indigo (Baptisia), and columbines (Aquilegia). Also Lenten and Christmas roses (Helleborus), lavender cotton (Santolina chamaecyparrus), candytuft (Iberis sempervirens), lavender, rosemary, southernwood (Artemisia abrotanum), and several other artemisias.