Fall is the best time to divide all except fall and winter-blooming perennials. Many (day lilies for example) perform best when divided every few years and doing so is an inexpensive way to have young divisions to plant or share.
A spading fork is the best tool for digging the plant to be divided since it pulls the root system while leaving most of the soil in the ground. A spade or shovel will work, but you will need to shake the excess soil from the roots. Begin at the drip line of the plant and dig down and inward. If the plant is very large, use a spade or shovel to slice it into several pieces.
The type of root system a particular perennial has will determine how to separate it. Once out of the ground, either pull small plants apart, or use a sharp spade or knife to cut them apart, leaving enough root system to sustain each new division.
Keep plants moist until they are replanted.