Chrysanthemums come in thirteen bloom types and a wide variety of colors. The flowers actually consist of masses of individual "florets." Disc florets form the center of the bloom, and ray florets extend outward from the center. In "incurves," the traditional "football" mums, the ray florets predominate and completely cover the disc. "Anemones," on the other hand, have large discs and just a fringe of rays. Come to our show and see them all.
Although mums bloom in the fall, you begin with rooted cuttings in the spring, and nurture them through the hot summer months. The winter is the time to plan your garden and learn all you can about the growing process.
There are many written and on-line sources of information about chrysanthemums. The National Chrysanthemum Society has several handbooks for sale, including one for beginners (which is sent free to first-year members), and membership in LICS-NCS includes a quarterly journal, appropriately entitled "The Chrysanthemum." Many fine books have been published about chrysanthemum culture, and we refer you to the bibliography on this site.
There are excellent online sources as well. The Wikipedia entry on chrysanthemums is quite informative. Of course, if you "Google" "chrysanthemum" you will find much more of varying quality.