Saving tomato seeds is slightly fiddly, but fairly foolproof. Note that F1 hybrids will not come true from seed. Cut a ripe tomato in quarters and scoop out the seeds into a little tub (a cottage cheese container is ideal). Add tomato liquid supplemented with water so that the seeds are floating in about a centimetre of fluid.
Leave to ferment undisturbed for no more than four days in a warm (but not roasting) place such as a window sill or hot press. The fermentation breaks down the gel sac around each seed and has an antibiotic effect on certain diseases.
A mat will form on top. Remove this gently and wash the seeds thoroughly in a sieve. Dry in an airy place for some days and store in an airtight container in a cool, dry room or fridge. You can add a sachet of silica or rice to absorb any residual moisture.