Most garden center mums, not florists' mums, will overwinter if properly prepared for. It is best to plant mums in the spring, to allow them to grow a root system with numerous stolons (horizontal stems that help the plant to spread). Of course, the fall is when we think of them and when they are widely available, so you can try the following steps starting in the fall.
Important factors are well-drained soil (left in a container they probably won't survive) and a location protected from drying winds. Any leafy plant benefits from watering before the ground freezes. Wind will desicate the plant if it can't draw water into the roots.
Just after a frost, when there has been some damage to the flowers, cut them back to 4 inches and discard the tops to avoid infection of next years growth. Once there has been some freezing weather, mulch them with leaves or straw. Keep them covered until the last frost in spring.
Mums should be fertilized regularly while growing until mid-summer. If you want the typical tight head of flowers, cut the tips back in the summer once or twice, lastly in mid July.