When you have grown the best tomatoes you've ever tasted, you might want to grow the same variety the following summer. If your tomato is an heirloom or open-pollinated variety, the seeds will reproduce "true to type," which means they will be an exact duplicate of their parent plant. But many plants are hybrids nowadays---their seeds can be infertile and usually don't yield the same fruit as their parent plant. When you want to save seeds from your annuals, start by purchasing seeds or plants that are not hybrids. Then you'll know in advance that the seeds you save will result in the same vegetables or flowers you first grew.
Harvest vegetables for seed saving when they are older than the ones you pick for eating. With flowers, wait for them to form seedpods or flower spikes and then snip off the pods or spikes when they appear brown and dry.
Scoop the seeds out of vegetables with a spoon and then rinse them in a sieve to remove all pulp.
Spread vegetable seeds on a screen you have propped up on bricks or pieces of wood. Make sure you dry them in an area that is warm, dry, well ventilated and out of direct sun. Most seeds will dry within one week.
Hang flower spikes containing seeds, such as the ones that basil forms, by gathering several spikes into a small bundle, tying them with string and then hanging them with clothespins from a line in a warm, dry, well-ventilated area out of direct sun. In one week or so, shake the spikes over a small box and the seeds will fall out.
Transfer your seeds into plastic zipper bags, seal them tightly and be sure to label each bag with the variety of seed inside. Store the bags in a cool, dry, dark place---your refrigerator vegetable crisper is a good location for saved seeds.