Here is the method that I have been using for years. I can achieve about 95% germination using this method. Use an old one-gallon ice cream bucket. Put 4 to 6 slightly over-ripe tomatoes in the bucket, and get an old board (a two-foot long 2X4 works well) and mash the tomatoes in the bucket with the end of the board.
Let the mashed tomatoes sit in the bucket for 2 to 3 days, at which time you should notice a whitish mold forming on the surface. Take a twig and stir the mold into the mixture. Let the mixture sit another day, and there will be new mold growing on the surface again. Stir it with the twig again, and let it sit for another day. After you have repeated the mold stirring for 3 to 5 days, the seeds are ready to remove from the yucky and smelly solution and dry. (It helps to ferment them in a garage, or basement, because they will stink by day two or three, and will probably attract fruit flies.)
You can remove the old pulp from the seeds simply by using a „panning for gold” method. Just slosh out the pulp and floating seeds over the edge of the bucket while replacing the lost water and pulp with fresh water. The viable seeds will remain on the bottom of the bucket. After all the pulp and floating seeds are washed out over the edge of the bucket, all that will be left is good seeds on the bottom. Carefully pour off all the water and put the wet seeds on a dinner plate to dry. It also helps to do this pulp washing with an outside faucet, letting the pulp and water simply go into the lawn where it will make no mess, and can be recycled into the lawn’s roots.
Your seeds that you have collected without fermentation will probably still sprout. Germination might be down, however. Plant extra seeds, and thin them out later if too many sprout. Experts advise us to use the fermenting method for one other reason also. Some tomato diseases are seed-borne, and the disease-causing agent (bacteria or virus) is contained in that gelatin coating around the seed. After the seed germinates, the new plant is re-infected by the same disease that its
mother had.