If you've had exceptionally productive or high quality tomato plants, chances are you'd like to reproduce those results in next years garden. Saving the best seeds from the best plants is the way to do this. If the tomato plant or plants are hybrids, I would suggest not wasting your time.
A hybrid is created by plant breeders who cross-pollinate different tomato varieties with the intent of producing a hybrid offspring with the best traits of the parent varieties. These seeds can be saved but the resulting offspring is frequently sterile, sometimes seedless and at times reverts to one of the parent cultivars when grown.
The best tomato seeds to save are heirlooms. Heirlooms are any variety that has been saved and grown for multiple generations. Heirlooms are Open pollinated or OP plants , Open Pollinated cultivars produce seeds / seedlings with the same characteristics as the parent plant. It is best to avoid hybrid or GMO tomato varieties when seed saving.
Saving heirloom tomato seeds is advisable. Fully ripe disease free heirloom tomatoes. The simplest way to do this is to squeeze the seeds out of a tomato onto a paper towel. The seeds are in a gelatinous sac. This gel enveloping the seed contains natural enzymes that inhibit germination until the seeds establish themselves in what nature deems to be a safe place to grow, such as crevices and cracks in the soil.
Once you've sqouzen the seeds and gel out, spread it evenly across the towel[s] and leave the towel and seeds in a shaded dry location untill completely dehydrated. No more gel, just seeds. Store your seeds still attatched to the paper towel in a jar or airtight baggy untill ready to use.
It's advisable to label the container with the date and cultivar. When ready for planting, cut the paper towel into segments with several stored seeds clinging to each section.
That's the simplest mode of saving and using tomato seeds. Some folks enjoy delving into all sorts of fermentation schemes and what have you. Fact of the matter is these schemes are unneccesary. They do improve the odds of success ever so slightly. In my humble opinion the benefit derived from these schemes does not justify the time, energy and expenditure with everythng else a gardener has to involve themselves with.
Fermentation of Tomato Seeds
The Fermentation process removes germination inhibitors and the gel sac from seeds, and it may treat some seed-borne diseases. The fermentation pocess is believed to extend the storage life of tomato seeds. Properly stored tomato seeds can be viable for 5 - 6 years with diminished germination rates exponentially over time.