It is not absolutely necessary to know how to divide crocuses; unlike plants that grow from rhizomes they do not choke themselves out by vegetative propagation.
Crocuses grow from corms, which resemble bulbs. Unlike a true bulb, which is a bundle of layered scales, a corm is a solid, fleshy modified stem used for storing nutrients. On the top of the corm is a bud or tip, from which the leaves and flowers will sprout. It is not absolutely necessary to know how to divide crocuses; unlike plants that grow from rhizomes they do not choke themselves out by vegetative propagation. Over the course of a growing season the plant uses up the nutrients stored in its corm, which shrivels. Below it a new corm grows. After blooming is finished, the leaves continue to grow and the plant stores nutrients in the new corm for the following year. Small offsets grow around the new corm; these are called cormels. Over a period of two years, the cormels will grow to become full-sized corms which will then produce leaves and flowers.
How to Divide Crocus
The only reason you would need to divide crocus is if you want to move some corms to a new location. To do this, dig up the corms in the fall after the first hard frost. Remove and discard the old, spent corm and separate the cormels from the new corm. Replant the new corm in the original location. Plant the cormels in a nursery bed and leave them there for a year. The next fall, dig them up; they will be almost full-sized corms by then. You can then plant them wherever you want a new patch of crocuses.