Since no one's answered you yet, and I hate to see a newbie waiting, I'll do my best! Tuberous begonias are, if memory serves, pretty easy to store over the winter (it's been a long time since I lived in a climate where they grew.) When they begin to dry off in the fall, let them go dry and store in a cool, but not cold, place, in mostly-dry peat moss or shavings or shredded newspaper, whatever's handy. Seems to me I hung mine in old nylons. Paper bags work. And for the record--all begonias will last with proper care--and maybe a litle luck!--so you don't have to replace any of them and can keep getting more and more!
Welcome to a wonderful plant family!

Thank you! I bought some for my sister-in-law too - I may go raid her garden to try and keep them for her over the winter too!