You can harvest the seeds of tomatoes, but it's a little different than harvesting the seeds of other vegetables. Almost all tomatoes grown today are hybrids -- a cross between two different varieties. The seeds of hybrids do not produce plants identical to those from which the seeds are harvested. If you want to harvest tomato seeds, you need to take them from open-pollinated or heirloom tomatoes. These are non-hybrid varieties which in most cases have been grown and passed down from generation to generation for hundreds of years. Heirloom tomatoes don't grow as vigorously as the modern hybrid varieties, but the tomatoes they produce are much more delicious. Plus they come in many different sizes, shapes and colors.
Cut the tomato in half and use a spoon to remove the seeds. Place them into a quart size jar.
Fill the jar half full with warm water. Cover loosely with plastic wrap or cheese cloth.
Set the jar aside for 7 to 10 days. Put it in an out-of-the way place that is not in direct sunlight.
Check the jar after a week. There should be a layer of white, moldy-looking material floating on top of the jar. The seeds should be settled onto the bottom of the jar.
Put the jar in the sink and carefully add water until the white moldy looking stuff overflows out of the jar, but not the seeds.
Pour the contents of the jar through a fine mesh strainer to remove the seeds from the water.
Spread the seeds out on a small plate. Put them in a well-ventilated place to dry completely. They should dry completely in about a week.
Package the completely dry seeds into small envelopes. Label with variety and date. Store in a cool dry place.