Here's how to save tomato seed: slice a very ripe tomato through the equator. Using the point of a knife, scrape and squeeze out the seeds and surrounding jelly into a glass. Add a half cup of non-chlorinated water. Take some tape and make a label with the variety and date. Now, leave it sitting around 2-3 days. The jelly will disintegrate. The top may grow a layer of mold. The good seeds will fall to the bottom. Take a mesh tea strainer and pour the lot through the strainer. Run some tap water gently through the strainer until the seeds are clean. Dump out the seeds onto a paper towel. Label the paper towel. Otherwise you may end up with several batches of mystery seeds. When the seed is dry, scrape it off the paper towel and put it away in a labeled envelope.
Lettuce seed is also easy to save. Like most tomatoes, lettuce is an inbreeder, that is the flowers mostly self-pollinate and the varieties breed true. Just let lettuce bolt and turn into a bush. The flowers turn into fluffy heads like miniature dandelions. When they open up at the base, as if to take wing, the seed is ready. Just pick it, pull off the fluffy top and store. By the time lettuce sets seed, all lettuce plants look like a scraggly dry bush, so it's good to label the plants while you still remember which is which.
With many new gardeners this year, and many gardeners switching from conventional to organic methods, I've been asked several times recently to explain heirloom vegetables. Heirloom vegetables are varieties saved and grown by back yard gardeners and small farmers, often for generations and sometimes for centuries. Since breeding and saving seeds is work, sometimes a lot of work, gardeners and farmers save the good ones: vegetables with a lot of taste, particular adaptation to a regional climate, or special cultural significance. There's no firm cutoff for age, so sometimes heirloom is used to refer to recent innovations such as the Green Grape tomato.
The home gardener looks for a really luscious tomato, and doesn't care whether it has the fortitude to survive machine harvesting and three days in a truck, followed by being stacked in the supermarket. The home gardener wants broccoli that produces a lot of fat side shoots after the main head is harvested and cabbages that are staggered in maturity. The market gardener, on the other hand, wants cauliflower that are all about the same size at once, so that he has some hope of filling 110 CSA boxes without giving some people a cauliflower the size of a basketball and others softball sized ones. The industrial farmer wants 10,000 identical cauliflowers all ready at once.
Heirloom vegetables are in general better tasting, less uniform and more interesting than that stuff in the supermarket which is bred to survive industrial farming, processing and distribution. There is no point in growing your own food if you grow the same cardboard vegetables that you can buy in the supermarket.
Vegetables can be either open-pollinated, which means that the seed can be saved and the next generation will considerably resemble the parent plants, or hybrid. Hybrid seeds are created by taking two different strains and deliberately crossing them. The next generation is called F1. The F1 often has a burst of hybrid vigor, resulting in larger plants.
Sometimes hybrids have other desirable characteristics, such as disease resistance or special color. Generally, the hybrid won't breed true, and may even be sterile. Just a basic plant cross, such as Mendel's yellow podded peas crossed with green pod peas, will have an F2 generation where half revert to the original parent varieties. Commercial hybrids can have very complicated parentage. Responsible seed distributors will label crosses F1. Sometimes you get the back story for open-pollenated varieties, such as "early tomato developed at OSU by Dr. James Baggett" (modern open-pollenated variety) or "frilly pink poppy carried over the Oregon Trail by Charlotte Aamots' great great-grandmother and saved for generations in the family back yard" (that's an heirloom, contact Susan Templeton, who has taken over stewardship of the Aamot fancy poppy, if you would like some seed.)
There is nothing inherently wrong with hybrids. Hybridization is the first step in plant breeding. Want a purple broccoli? Cross broccoli and red cabbage and select plants to save seed from year after year. Eight years of work later, you have a stabilized variety which is purple headed, grows like a broccoli and heads the first year, and breeds true.
Tomatoes seeds are easy to save because modern tomatoes are inbreeders. Each flower has both male and female parts, and each flower self-pollenates to produce a fruit. Save the seed, and you get the same genetic material that you started with. Some older tomato varieties cross more easily, indicating that tomatoes were once partial outbreeders.
Inbreeding plants, like tomatoes, peas, beans and lettuce, are easy to save seed from: just select seed from a sturdy looking parent plant. Outbreeders like squash are similar to people: you know who the mother plant is but the father is harder to pin down. Fortunately, squash has big flowers with separate males and females. The female flowers have a tiny fruit at the base. If you want to pollinate it deliberately, tape a female flower shut just before it is ready to open. The next day, use a paintbrush to move pollen from a male flower that opened that day to your female flower, and tape the female back shut. Summer squash, gourds and small winter squashes such as the Sugar Pie pumpkin are all Curcubita pepo, and will all cross. A summer squash-gourd cross will make people sick. A summer-winter squash cross is probably just not very good. To save your own summer squash seed, hand pollinate. You will have to let the fruit go well past anything you would want to eat to get mature seed, and the vine will stop pumping out fruit when it switches to growing the seed. The product of your work is a monster zucchini with huge, tough seeds and stringy flesh. Cut open the monster and dry the seed.
More seed another time.