One can easily save seeds from ripe tomato fruits by simply removing the seeds from fruit and allowing them to dryout. However I reccomend that the seeds go through a fermentation process. Fermenting the seeds will help to remove the gelatinous coat which contain gemrination inhibitors and helps reduce or destroy any pathogens present. This helps seed longevity and reduces the chance for disease being spread.
Selecting Fruit for Seed
Seeds are ready for extraction once the fruit reaches the "breaker" stage. This is when a small amount of color (usually red) shows up at the blossom end of the fruit. Still it is probably best to wait till a fruit has obtained it's full color.
Things to avoid:
Extracting and Fermenting Seed
Extract the seeds from fruit with some of the juice from the tomato by putting them in a marked container. Rely on the fruit juices for moisture but add a small amount of water if needed to prevent drying when fermenting. Too much water and the could start sprouting.
8oz-16oz plastic containers with lids (which will help too keep out insects, prevent spills, hold moisture and reduce odor issues) work well but one can use a cup or even a plastic bag. Be sure to label the container and not the lids/covers as they can get mixed up if they fall off or get moved around. If one does use coverings, the container should not be set in direct sunlight. They may get too hot and harm the seed.
In a few days mold should start to form on the surface of the extracted seeds and juice. The warmer the temps, the quicker they ferment. Usually this begins in about 2-3 days. More may be needed in cooler conditions. There is no "set" time for when they will start but if the mold has formed it is best to get them rinsed and cleaned within the next day or so. Once that protective gel on the seeds gets broken down they could start to take up water and pre-sprout.
Cleaning, Drying and Storing Seed
A mold should start forming on the surface but if it does not and its been 2 days that's ok. Just rinse the seeds well in a strainer and them tamp then out to dry. One can do so on paper towel, a plate, a screen or various other methods. It is important to dry seeds slowly, since rapid drying out shrinks the seed coat around the embryo and reduces seed quality (in terms of vigor).
Good seed should be a light tan color. If you get dark brown seeds they may have set too long and germination will likely be reduced. If this happens do not worry too much, usually some will germinate the next year and there is some genetic variation for seed color as well as seed size.
Store the seeds in the refrigerator and they should keep well for about 4 years. One can still get viable seeds 7-12 years later but usually the germination percentage is lower. If one plans to save seed this long be sure to save plently of seed. Reducing the humidity will increase seed life. This is done by adding a desiccant like silica to a container which will hold the packets of seeds. One can get desiccants from the packets of silica that come packed in electronics.