There are different procedures for different plants. I suggest you borrow a book on seed saving from your local library, that is where I got my information, that and on line.
jackb
Obviously, some things have seeds that are easy to spot; they are part of the plant when we harvest them. Tomatoes and peppers, beans, peas. Other vegetables are usually harvested before they make seeds, like spinach and lettuce, radishes and carrots. Those vegetables, you have to purposely leave some plants to make seed, and keep an eye out so you can get the seed before the birds or bugs do. Jack has the right idea. There are books and lots of things on the net that can show you how to collect and store seeds. Keep in mind that saving the seeds of hybrid vegetables may not give you the same type of vegetables that you grew originally. Some may be satisfactory, but seed from hybrid tomatoes and peppers are often not worth growing.
She is a fabulous role model! And after you learn how to save seed, the next step is breeding your own varieties . . . and you will already have the book on how to do it!
(Full disclosure: I only know of Carol from a distance - she is not a close friend and I have no financial stake in paper publishing. This is just an honest, good opinion . . . and yes, I do own a copy.)
I am also trying to find fellow gardner folks who want to trade seed. For example, I have 50 heirloom California Wonder green pepper seed (and a few other seeds) from my garden this year that I'd give to people. I'd like to find others willing to do the same with other seeds they have. I was hoping this seed trade could work out for all of us spreading the gardening bug.