You can save the seed from many flower, vegetable, and herb varieties with great success. The list below suggests some common plants that are easy to grow for seed-saving, although many others exist. After harvest, you can store your seeds in paper envelopes or plastic bags.
Peppers: Harvest the peppers when fully ripe. Cut into the pepper and scrape the seeds out and onto a paper plate. Let the seeds dry at room temperature in a single layer on the paper plate.
Beans: Any non-hybrid bean variety can be dried on the plant for seed. Allow the bean pods to remain on the plant until the plant dries in the early fall. The bean pods will be dry and shriveled. Remove the beans from the pods.
Peas: Peas may be saved for seed in the same manner as for beans, described above.
Tomatoes: Tomato seeds have a gelatinous coating that needs to be removed before the seeds may be dried for storage. The easiest way to do this is to ferment the seeds with some water in a warm, sunny place. When fermentation is complete the tomato seeds can be dried and stored for next season. For a tomato seed fermentation tutorial, see here.
Basil: Let your basil plants send up flower stalks near the end of the growing season. Pinch off the flower stalks when they begin to dry and become brown on the edges. Allow the flower stalks to dry at room temperature for a few days. Then, gather the basil seeds by tapping the stalk gently on a paper plate. Tiny black seeds should shake out of the stalk.
Cilantro (coriander): Coriander is actually the dried seeds of the cilantro plant. Chances are, your cilantro will produce enough seed for you to use some for planting and the rest for cooking! After the cilantro flowers at the end of the growing season it will begin to produce seeds. The seeds are ripe for harvesting when they have just begun to turn brown. Cut off the cilantro stalks and allow the plant and seeds to dry fully in a paper bag, then collect the seeds.
Calendula, Marigold, and Nasturtium: These flowers each effortless produce an abundant amount of seed when they are done flowering. Before hard frosts hit your area collect the dead flower heads and place them in a paper bag. Let them fully dry in the bag then collect the seed.