Let your tomatoes get very ripe.
Cut tomatoes in half, and scoop out the seeds and all the jelly-like stuff around them into a jar.
Add a little bit of water to the jar, then cover with cling film and make a hole or two in the cling film. (some instructions don’t mention water or cling film – there are different ways of saving seeds)
Leave the jar somewhere fairly warm for a few days, stirring the mixture a couple of times a day, allowing it to get fairly smelly. The fermentation process helps to kill off diseases carried by the seed.
Add a fair amount of water to the jar. This sorts the viable and non-viable seeds, as the best seeds sink to the bottom. Scoop off those that float to the top and then tip the others into a sieve and rinse to clean them.
Tip the cleaned seeds onto a ceramic or glass plate and leave to dry thoroughly. Then you can pack them, and label them and they should last for a while.