Mums are amazing flowers and I am a huge fan! In Southern California where it doesn't freeze mums are also fairly easy to grow. Chrysanthemums are in the daisy family (the Asteraceae) and aren't actually flowers but rather an inflorescence (hundreds of small flowers that give the appearance of a single flower). You don't have to care about that, just sort of interesting. The fancy mums that I prefer are all grown by cuttings. Though it is possible to save mum seeds and breed your own, that's not something I have any experience with. Mums used to be prized flowers in backyards across the country but fell out of favor (I blame grocery store mums for giving them a bad name and the cultural shift away from backyard growing that happened all over). I'm so grateful to those committed mum growers (thank you Chrysanthemum society members and Kings mums!) kept these beauties around. In fact, a GREAT resource about all things mum is your local Chysanthemum society. Find one near you and join! They abound!
If you don't live where U.S. mum suppliers ship, your best bet is to get cuttings from another grower. Mum cuttings are very easy to propagate. Make sure to obey all the long list of laws about moving plant material (of course!).
I don't need to do anything special for my chrysanthemums to keep them alive in the winter but for those in cold climates, you need to protect your mums from freezing. Pot them up and bring them inside. They will need a light source so plan accordingly. I remember living in Minnesota you could tell the gardeners because of the bright light shining from their windows keeping their indoor plants alive in the winters. Another reason I'm glad to live in Southern California (except for peonies. I'm sad for the absence of those). Anyway, grow some mums! They don't have a problem with our dry weather. For those in wetter climates you might need to do some fungus prevention. Order in the winter, plant in the spring, cut down to 4-5 leaf nodes by Fourth of July and then enjoy stunning flowers all fall. Easy!