While we don't save seeds from every annual crop that we grow, we do strive to preserve the genetic material for a signifigant portion of what we grow. Amoung the easiest seeds to save for the following year are tomato seeds. The complete flowers of tomato plants almost never cross polinate (except currant varieties) so you can save seeds without isolating plants.
To save tomato seeds the first step is to ferment them. After separating a bunch of seeds from the flesh of a tomato one will notice they have a clear coating around them. This coating inhibits growth and can be removed quickly through fermentation. The process of fermentation only requires putting the seeds in a jar with a little water for 3-5 days until a white mold forms on the surface.
After the mold forms the seeds are ready for drying. We usually pull off the moldy surface and discard it, then add a little more water to the solution stirring it around. Next we put a coffee filter in a colander and pour the tomato seed solution into the coffee filter. After a couple hours the liquid has run through the filter and all your a left with is the seeds (and a little pulpy crust).
We leave the seeds on the filters to dry more completely for a couple days. Once the seeds are dry we divide them into piles of 20-25 seeds and put them into coin envelopes.
Each small seed pack has more than enough seeds to start plants for that variety the following year. By keeping our seeds in the freezer the germination rates remain high for 5-10 years. This enables us to keep the extra packets for future years so we don't have to save every variety of tomato every year.