To ferment the seeds, add about half as much water as there are tomato seeds and juice in the bowl and stir the mixture twice a day for about 3 days. Keep a close eye on the mixture—especially if it’s a warm area, as fermentation happens more quickly at high temperatures. As the mixture ferments, its surface will become covered with white or gray mold. Don’t keep the bowl in the kitchen, anywhere it can be tipped over by animals or children, or where you’d be able to smell it—it will get pretty rank.
When bubbles begin to rise to the top of the mass, or when a thick coat of mold has formed, stop the fermentation by adding enough water to double the mixture, and stir vigorously. The clean, good seeds will settle to the bottom of the bowl. Gently pour off mold, debris and any seeds that float (they're hollow). Add more water and repeat the process until only clean seeds remain.
Capture the seeds to be saved by pouring the liquid through a strainer, wipe the strainer bottom with a towel to remove as much moisture as possible, then dump the seeds onto a glass or ceramic plate to dry. Stir twice a day to ensure even drying and to prevent the seeds from clumping together. Warning: Tomato seeds will germinate unless you dry them quickly. To speed drying, you can use a fan, but don’t put the seeds in sunlight or an oven.
Here's a step-by-step:
To save seed from a ripe isolated tomato, cut it in half and squeeze its juice, seeds, and pulp into a glass container. Wait three to five days until the surface is covered in whitish mold. Scrape off the mold with a spoon, leaving the seeds.
Add clean water to the seed mixture and stir. Viable seeds sink to the bottom and nonviable seeds float. Remove floating seeds and then pour the good seeds into a fine mesh sieve.
Rinse the good seeds repeatedly until they are clean and no pulp remains.
Spread the clean seeds onto a paper plate or coffee filter to dry for three to five days. Stir twice daily to promote even drying. Store dry seeds in small manila envelopes.
Don't forget to label with the variety and date.
Keep reading: 10 Tips for Storing Seeds