Hardy perennials grown as annuals in colder climates, garden mums thrive in rich, well-drained soil in full sun. They also need adequate water and weekly fertilizing to bloom well. Mulch thoroughly with shredded leaves or dried lawn clippings to conserve soil moisture and deter weeds. Plant garden mums in spring for full, bushy fall plants. Starting when plants are 6 inches tall, pinch back tip growth 1 inch every month until midsummer to encourage good branching and blooming.
Perennial mums are easily propagated in spring by root division. Lift the entire clump and with a very sharp knife slice it into wedge-shaped sections, like a pie -- cutting off and discarding the "tip" of each piece, the older, center part of the original plant. Replant the rest of each slice as separate new plants to expand your bed or pot them up as gifts, watering roots well. You can also take 5-inch cuttings in spring or early summer, remove leaves on the lower half of each stem and then root these in moist perlite.
Mum seeds aren't always as obvious as seeds produced by other plants. After mature flowers have fully dried on the plant, carefully remove the flower head and place it in a pie pan or similar container. Carefully pull away the outer sections of the dried flower head "fluff" with no seeds, working your way toward the center of the flower, where the seeds are. Place the seeds and fluff into a paper envelope or small paper bag, and label and seal it.
If you've saved seed or buy chrysanthemum seed, germinating it is fairly straightforward, as you can keep soil as a constant temperature between 70 and 75 degrees Fahrenheit, such as with a propagating mat generating heat under seed flats. Sow seeds evenly on top of sterile planting soil. Do not cover them. If using saved seed, press seed and fluff together onto the surface. Water well, keeping the soil evenly moist. When seedlings have four to six leaves, in six weeds or so, transplant individual plants into 2-inch peat pots.