Be sure the seeds are perfectly dry so they don't mold. Store them in tightly capped small bottles, in a cool place
Most seeds need a "rest period" of one to several months before they will germinate. After that, germination can be tested by soaking 10 seeds, draining them, and spreading them between layers of moist cloth. Keep the cloth moist. Germination varies between two days and two weeks depending on the type of seed and temperature.
The percentage of germination decreases with age. Seeds of corn and onions can be stored for two years; peas and beans for three years; tomatoes, four years; cabbage and spinach, five years; and beets and squash, six years.
Save the best seeds, from parents with the qualities you desire. The earliest pea pods can be marked by tying a scrap of colored yarn or similar material on the vine, a sign that says these pods should not be picked. When the pods are completely ripe and dry, pull the vines and hang them in a garage or shed. When the pods are brittle shell and store the peas.
Mark chosen tomatoes and leave them on the vine until they are overripe, but pick them before they spoil. Cut the tomato and remove the seeds. Some pulp will inevitably come along. Soak the seeds and pulp in water for about two days or until they start to ferment, but not long enough to sprout. Separate the seeds from the pulp by rubbing, and dry them quickly (but not in direct sun) by spreading them thinly on newspaper.
Carrots, radishes, and other biennials will not produce seed until the second year of growth. These can be left in the garden over winter under a heavy mulch, or they can be dug and stored in damp sand in the root cellar for spring replanting. If they will be in the way of future tilling or succession planting, consider a separate area for seed production. When the seed head is almost ripe, tie a paper bag over it to collect those seeds that will otherwise fall to the ground.
Onions are also biannual, but producing bulbs or sets requires yet another year. Sow seed thickly - about a quarter of an ounce in four square feet - so they will not get too big. When the tops fall over pull them and store them in net bags for planting the following year.