Early fall is a great time to divide perennials that are showing signs of overgrowth. They might not be flowering as well anymore or possibly hollowing out in the center of the clump. Some perennials can reach this stage in just a few years while others can take much longer. In general if you grow your garden in good fertile soil and choose vigorous plants you will have to do this chore more often. It is wise to allow most plants to develop for at least 2 or 3 seasons before dividing to allow them to bulk up enough to handle the stress.
Very mature clumps of perennials can be difficult to dig up which is why it is better to divide your perennials before they get to this stage. Ornamental grasses are one of the most difficult and may need a very heavy boot! Once in awhile if you just want a piece to move to another location you can steal a piece off the edge of the clump. Using a sharp spade cut a wedge from the edge and remove then fill the empty space with fresh soil.
To divide your plant first water it the day before, cut the foliage back to about 10 inches then dig it up with a sharp spade digging wide and deep enough to capture all its roots. Shake off the soil from the roots so they are more visible.
For spreaders with runners it is best to cut them apart in patches rather than trying to pull the runners apart. That usually leaves you with a mess of damaged roots that are hard to replant.
For perennials with tightly packed crowns wash the clump off with the hose to further expose the crown. You will not likely be able to pull them apart so you will have to cut them apart instead. Observe the crown to see where it separates naturally and using a sharp serrated knife follow these lines. In order to grow, each new part must have its own roots and at least one bud or shoot.
For extremely large crowns you may need to use an ax or spade. If possible cut down the middle then continue to divide these sections into your desired size.
Once you have your plant divisions inspect them for weak parts or weeds. Divisions of plants should be replanted as soon as possible so they do not have a chance to dry out. Plant their crowns at the same depth as the original plant and water well.