To save a small quantity of seeds for your own use
Remove seeds from the fruit and rinse in a sieve under cold running water, rubbing them against the sieve to remove the gel coating. Spread them on a paper towel or piece of kitchen paper and leave to dry. Fold up the paper, label it, and in the spring pop the paper with the seeds attached on to moist compost in a seed tray to start your plants. I have drawn boxes the size of the seed packet and have placed the seeds on the kitchen paper before then cut up once dry, but prefer the Fermentation Method
To save a larger quantity of seeds for Seed Circles I use the Fermentation Method
Squeeze the pulp from ripe tomatoes into a suitable container (e.g. a large yoghurt pot or KFC Gravy or Beans container). You can also process ripe fruits into a food processor with an equal quantity of water until you have a pulpy mass. The seeds are hard and will not be damaged.
Put the container into a warm place to ferment. It may smell bad but it is good for the seeds. Fermentation removes compounds that inhibit germination and it also destroys seed-borne diseases. You are merely duplicating what happens in nature.
After three or four days, when the container is topped with a mass of mould, add plenty of water and stir vigorously. Good seeds will settle to the bottom, so you can tip the rotting mass away. Rinse and repeat until only good, clean seeds remain. Strain the water off and place them on a clean plate or piece of glass or KP Nut or Gravy plastic lid (they will stick to paper). Stir once or twice a day to promote even drying and prevent clumps of seeds forming. Dry the seeds quickly to prevent them germinating, but avoid direct sunlight or an oven. A cool, gentle breeze is best I place mine on top of the fridge next to an air brick.
Storage Tomato seeds will last in storage for about six years, depending on the variety.