They're advertised as "hardy" mums, and technically they are, but in reality they're not. Confused yet? Hardy mums usually don't come back next spring because they are forced into bloom and expend so much energy with all those flowers, they can't establish roots.
So here's what I do to make them last as long as possible, and mums can often bloom well into winter, they are tough. When choosing a plant, pick one that is just budding, I bought the plant above two weeks ago before there was even a blush of color. You can look at the tag to see what color it is and usually compare it to the same variety that's further along at the nursery. That's where I go too, is a good nursery, especially if I know they grow the mums on site instead of having them shipped in.
Once home, I immediately pot the plant up in a container at least twice the size of the current pot. They are fine to plant right in the garden too, just put them in a spot with full sun and good soil. If the ground isn't good, but a couple bags of compost and improve it.
Never let them dry out and don't overwater either.
The sooner they are planted the better, if you're lucky they will catch on and return next spring to bloom year after year.
The "real" way to get mums to come back year after year is to plant them in the spring. They well become established and there will be no stopping them. It takes some maintenance though; the buds have to be trimmed off two times during the growing season if you want your plant to flower in the fall. Without the haircut they often bloom in early summer. Cutting the plant back forces it to make more and more buds that will explode with color in late September.
For the plants bought now, let them bloom and pick off the spent flowers to encourage more buds.
I never seem to have the time to cut back my spring planted mums and I don't mind buying them at the end of the season, usually a little less than half will make it through the winter, but that's OK. I love the colors in the fall and want to keep gardening until it really gets cold.