Strawberry with seeds.
image by grendelkhan: flickr.com
Not all strawberry seeds are equal. Today, most seeds are produced from F1 hybrid plants, which are created by genetic engineering. When these berries are propagated, they're not likely to bear fruit anything like the ones that the seeds or runners were harvested from. The offspring revert back to an earlier ancestor, with characteristics that you probably won't like. However, if you buy either open-pollinated, or "OP" plants or seeds, they'll grow and reproduce true to variety. The seeds of open-pollinated strawberries can be saved to produce identical plants generation after generation. Seed packet labels state whether the contents are F1 or OP varieties. Your best bet for sustainable seed reproduction is to purchase OP varieties such as Fresca, or any of the Alpines.
Monitor your strawberries as they ripen. Allow the fruit to mature on the plants to the point of being mushy, when they're past being useful for eating.
Pick the overripe berries and put about 1 cup of them in the blender with 1 cup of water. Process on high for only a few seconds to avoid damaging the seeds. Wait a few minutes for the mixture to settle. Viable seeds will settle on the bottom, while unripe or sterile seeds and the pulp will float to the top.
Strain the liquid through a coffee filter and discard. Press the remaining pulp through a sieve, retaining only the seeds. Rinse the seeds in the sieve under gently-running cold water.
Spread the seeds out in a single layer on a thick paper towel to drain them for a couple of hours. Place them in a ceramic bowl to dry out so that they can be safely stored. When they no longer stick to each other and you can move them around the bowl easily, they're dry.
Label paper envelopes and store the dried strawberry seeds in them until you're ready to plant. Put them in a dark, dry location. They'll remain viable for about two years.