Saving seed from your garden is a very simple process. However, you do need to do something that is probably in contrast to what you would normally allow happen ..... allow some plants complete their life-cycle and produce seeds.
For many gardeners, this means allowing the plants to go beyond the stage that they would normally allow them to. This will mean that sometimes the plants will not be as visually appealing as they might normally be. Perhaps they will be taller, browner and more "straggly", or perhaps rather than picking the fruit, it means allowing it to become over-ripe to the point of "rotting".
However the plant looks, it certainly means not doing what you may have normally done .... picked the fruit, pruned it or perhaps even removed it. You need to allow it to complete it development up to the point where it's seeds have been produced and are mature within either the fruit or a seed pod.
Step 1 - Allow the plant to grow and produce its fruit or seed pods.
Step 2 - Allow the fruit or seed pods to fully mature.
For fruit this will mean that they have fully ripened. For seed pods, in many instances this will mean that they turned brown and dried.
Step 3 - Remove the seeds.
For fruit, this will usually mean that you simply scoop them out of the ripened fruit and remove as much pulp as possible. For seed pods, it will usually mean breaking open the pods and collecting the seeds - a possible way of doing this I will address further below.
Step 4 - For many fruit, allow the seeds to dry.
Step 5 - store the seeds in a dry location. I usually use a letter envelope to store the seeds in.
Step 6 - Plant your new seeds during the next growing season.
Most seeds can be stored for 1 to 2 years, but this is not always the case. The following website gives you some guidelines for how long many seeds can be stored: How Long Do Garden Seeds Last.
If your seeds are quite small, collecting them can sometimes be quite tedious. A simple way of overcoming this is to place the pods into a plastic bag and then; witn the plastic bag, crunch them up. This will cause many of the seeds to be removed from the pods. You can then use something like a colander to separate the seeds from the seed pod husks.
A Fact Sheet about saving seed can be downloaded from: Saving Seed From Your Garden Fact Sheet
The following video demonstrates this process.