When you have a really good, healthy tomato plant that produces lots of flavorful fruit and resists disease well, you may want to save seeds from the plant to sow in the garden next year. Tomatoes are self-pollinating, which means that seeds will produce clones of the parent plant unless it was pollinated by a different plant. It's also possible to save seeds from a tomato bought at the market, though to insure success, make sure the tomato was vine-ripened and not harvested while green.
Wash the tomato and slice it across the middle. Squeeze all of the pulp out into some cups. The cups should be about half full. If you're saving seeds from more than one type of tomato, make sure the cups are labeled ahead of time.
Put the cups outside in a shady place, or indoors where fruit flies and the smell of rotting tomatoes won't bother you. The pulp has to sit for several days and it doesn't smell nice. Check the pulp every day to make sure it's not drying out in hot weather. If it looks dry, add a little water.
Leave the cups sitting out until a layer of white mold appears on the top. Gently scrape the mold off with a spoon and dispose of it. Be careful to not scoop out any seeds when you do this.
Fill the cups to the top with water and stir them. The good seeds will sink to the bottom. Throw away the seeds that float.
Rinse and drain the seeds well. Fill the cups with water a few more times and dump out the water while holding the seeds in. When all the pulp is off the seeds, put them in a strainer and rinse them again.
Spread the seeds onto plates to dry them. Be sure to label the plates with the type of seeds that you place on them if you have more than one variety. Set the seeds out in a shady place for a few days until they are completely dry. Stir them every day to make sure they don't stick together.
Store the dried seeds in labeled airtight containers. Put them somewhere that is cool, dark, and dry until it's time to sow them in the spring.