The following is not meant to be, by any means, a comprehensive guide to seed saving but to give you general idea of the process. There are many good books and websites you can turn to for the detailed information you will need to be successful. Certain techniques must be adhered to, such as how far apart closely related plants should be to prevent cross pollination and how many different plants of each type of vegetable to take seed from to maintain genetic diversity, and a good book or website will walk you through the process.
Types of plants
Plants fall into three basic categories: annual, biennial, and perennial. Annuals grow and produce seed in the same year and then die. Biennials grow in one year, produce their seed the following year, and then die. Perennials live for varying numbers of years, depending on the kind.
Annuals
Annuals are relatively simple to save seed from. The annuals that produce a fruit that we eat (tomatoes, peppers, cucumbers, squashes, and the like) are easy, but each one has specific rules. Ripe, red peppers get cut open, and the seeds are scooped out and put on a plate to dry. Ripe tomatoes have the seeds scooped out and placed into a bowl of water for a day or two. Strain them several times to remove the pulp, and then let the seeds dry. Cucumbers are similar to tomatoes with the bowl and water technique, but the fruits are left on the vine until they turn yellow. Choose the biggest and best specimens to save for seed. For annuals like lettuce and broccoli, allow several plants go to seed; they will get quite tall and develop flowers and then seed heads.
Small potatoes about the size of a walnut are saved separately in the cardboard boxes with the other potatoes in the cold room and planted in the spring. Make sure the potatoes are free from nicks or other damage, or they may not survive until spring planting time. Garlic gets planted in the fall in my area, so not all that long after harvest, the largest heads get separated into cloves and go into their new bed about mid-October.
Biennials
Biennials like carrots, parsnips, beets, rutabagas, and onions need to be overwintered in a protected place. I have a separate crate with damp sand in the cold room for the seed vegetables, except the onions, which stay in the main, unheated basement. Choose the biggest and best specimens to save for seed. These get planted in a seed bed the following spring where they will shoot up seed heads that will develop and dry over the summer. Biennials such as Swiss chard and cabbage are dug up with the root ball intact and placed into pots in the cold room.
Many years ago, an old Canadian farm wife showed me the cold room in their basement. It was a small room off the main cellar, and it had a dirt floor. The cabbages and celery actually got planted in the dirt until the spring. So cool.
Perennials
Perennials just keep going. Fruit trees, for example, can last decades. Blueberry bushes can last twenty years or more. The same is true for asparagus. Raspberries are shorter lived and may need to be replanted after eight or ten years. Perennials generally don’t get started from seed, so don’t worry about saving seed from them.
There is so much more to tell that space here simply won’t allow. Buy a book or download the information you will need.