Check your coreopsis plants for blooms. The seeds form directly from the blooms, so the more blooms, the more seeds. Continue to check the blooms periodically and note when they begin to wither.
Check the withering blooms periodically, watching for their centers to turn dark brown. This generally happens about four weeks after the flowers have withered. When the centers are dark brown and have a dried appearance, cut the withered blooms off their stems and bring them inside.
Remove any remaining petals to fully expose the seed heads. Spread the seed heads out onto a tray that you have lined with newspaper or paper cut from a brown grocery bag. Place the tray in a sunny window or some other warm, dry area of your home and let the seed heads dry out for approximately three days.
Hold the seed heads over the tray and break them open, one at a time, by gently crushing them with your fingers. The seeds will fall out onto the tray.
Place the contents of the tray into the kitchen sieve. Gently agitate the sieve until the debris falls out, leaving the seeds in the sieve.
Some larger debris may be left in the sieve. If you'd like to remove the larger debris, transfer the sieve's contents into a deep bowl and take it outside. Gently blow into the bowl, and the debris will fly out, leaving the seeds behind. Keep in mind that the seeds are very small and lightweight. If it is a windy day or you blow too forcefully, your seeds may blow away with the debris. Another option is to simply leave the debris in with the seeds.
Transfer the seeds into a paper seed packet for storage. You may use a plastic zip-top bag for this purpose; however, there is a risk of moisture getting trapped in a plastic bag, and moisture can cause your seeds to mold or rot.