Beets grow from seeds, but you can save beet seeds from the prior year if you wish (as long as the variety isn't a "hybrid"). Store a few good-size beets through winter and replant them in the early spring. Let the beet plants grow flowers. The flowers will be quite tall so you'll need to stake them. After they grow spikes, snip off the ends to help the seeds mature. As the spikes turn a brownish color and dry out, cut them and place them in a paper bag in a warm, dry place. After two weeks, rub out the seeds. Store in a cool, dry area of your house such as the back of a large refrigerator.