Answer: This is a biennial. It will self seed if you leave the flowers on the plant. The flowers will fade and dry up, and seeds will form. They will naturally drop off the plant and plant themselves.
Some of the fallen seeds may germinate this fall, some will germinate next spring. Seedlings that appear this fall will bloom next spring. Seedlings that begin growing next spring will bloom the following year. This way, the patch reseeds itself on an ongoing basis.
If you want to save seed, wait until the seeds are ripe and about to drop on their own. At that time you can scatter them in the area where you want more plants, or you can save them to start as you did the first time.
Your other option is to transplant some of the new seedlings that grow in the garden. In my opinion, this is the easiest way to start a new patch of sweet Williams. There is no point to transplanting the existing plants -- they will die out soon now that they have bloomed.
Enjoy your flowers!
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