Although many very experienced gardeners save seeds from their flowers, saving seeds from vegetables can be a bit more complicated. Unfortunately, it is not a good idea to save seeds from all of the vegetables you grow. How then do you decide when NOT to save seeds?
Some vegetables for which seeds and plants are sold are hybridized. The theory behind hybridization is that by creating a hybrid, it is possible for botanical geneticists to take the best qualities of one variety of a vegetable and combine that with the best qualities of another variety of the same vegetable.
Why is this done? Quite simply, hybridization makes it possible to improve on nature by making certain vegetables more disease resistant.
If hybridization improves the disease resistance of a particular plant or vegetable, then why not save the seeds? Quite simply, it isn't possible to ensure that the seeds harvested from a hybrid plant will be pure. There's always the possibility of cross pollination. There is also the fact that some plants are particularly predisposed to certain problems.
By trying to grow seeds from a hybrid variety of a vegetable, it is distinctly possible that you will be reinforcing the diseases or problems that the hybridization was trying to prevent. Most good nurseries will indicate on the plant labels when the plants are hybrid varieties. The most disease resistant tomato varieties are typically hybrid varieties.
Some varieties of lettuce may be hybrids. A dwarf variety of Cos Romaine lettuce is likely a hybrid because Romaine originated on the Island of Cos in the Mediterranean Sea. It wasn't a small variety of lettuce, but rather one that grew in compact heads that typically grow upwards rather than outward.
Lettuce isn't prone to diseases the way tomatoes are. Any vegetable that is prone to diseases - whether bacterial, fungal or viral is one for which I'd be reluctant to save seeds. Unless you have a set up whereby you can separate your crops and keep a sufficient distance to make any possibility of cross pollination impossible, you can never be certain that you haven't unwittingly produced a hybrid on your own.
What are the best vegetables from which to harvest seeds? Any type of heirloom vegetable will always be pure. Heirloom vegetables are bred to perpetuate the original variety. When seeds are planted so that new seeds can be harvested from the newest crop, they are planted in a manner that will prevent any possibility of cross pollination.
Any seed manufacturer goes to great lengths to ensure that all of their vegetables are always planted in rotation to prevent soil born diseases from being continually transmitted to new plants through the generations.
Allow heirloom varieties of vegetables to bolt or go to seed so that you can harvest their seeds. If you find an exceptional pepper, maybe allow one plant to go to seed so you can harvest the seeds. If you grow a really unusual variety of lettuce that you decide you love, allow a single plant to bolt so you can harvest seeds.
Herbs are also a wonderful resource for saving seeds. Whenever I find a special herb - a variety of basil whose flavor really speaks to me, I will allow some of that plant to go to seed so that I can harvest the seeds.
If you can't save seeds from a plant, there is nothing to say that you can't try to propagate it by rooting a cutting. Propagation is one way to reproduce the plant without risking the problems associated with hybridization or disease resistance. If the stems on the vegetable you wish to propagate are woody, the best way to get the cutting or cuttings to root is to dip it into rooting hormone.
After harvesting seeds from your vegetables, you need to allow them to dry out completely. Remove any flesh or leaves from the seeds before you dry them, if possible. If not, separate this stuff after the seeds are completely dry. Before going to store the seeds, make sure they are completely dry. Store them in a place that is NOT closed off to air. If you put seeds in an air tight place, even if the seeds are completely dry when you put them in the container, if moisture gets in, they will mold.
Know that the seeds you save from one season will likely only be viable for one season. If you want to test the viability of seeds, you can do so using the plastic baggie method.
Take a paper towel and moisten it. Wring it out so it doesn't have too much water in it. You want it to be damp but not soaking wet. Fold the towel in half. Place the seeds inside the half of the paper towel and fold it over again. Fold all the sides over so that the seeds are in a little envelope type thing.
Place the moist paper towel with seeds inside in a plastic baggie and put the baggie in a warm and bright place. Check the baggie in a few days to see whether the seeds have sprouted. If they have sprouted, plant them in a small container so you can see how well they grow.
If they haven't sprouted, put the seeds back in the plastic baggie and check it again in a few days. If after a week or two, the seeds haven't sprouted, it is likely that they aren't viable and won't sprout. You can try this process again with different seeds to see if the results differ, but if the second batch of seeds don't sprout, I would conclude that the seeds are sterile.