The following information is from Ohio State University Extension Service: Harvest begins in mid-September and can run into October. A check of the flower head will indicate maturity; florets in the center of the flower disk are shriveled, heads are down-turned, and a lemon yellow color is on the backside. Pull a few seeds and split them with a knife to check if seed meat has filled. Poorly filled seeds may be due to a lack of pollinating insects. To harvest, cut the seed head with about a foot of stem attached and hang in a warm, dry, well-ventilated, rodent and insect-free place. A paper bag with holes or cheesecloth can be placed over the heads to catch falling seeds as they drop during drying. Seed heads can be allowed to ripen on the plant, but cheesecloth or nylon netting will be needed for bird protection. Once the seed is dried, it can be rubbed easily from seed heads. Humidity levels must be kept low to prevent spoilage. As a side note, your sunflowers grown from this seed may not look like their parent plants, especially if they were a hybridized variety.
