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The Seed Saver's Bible" is a worthy investment if you intend to seriously save seed.
If you only wish to dabble, then winter squash and pumpkin seeds are easy to save and have a good sprouting rate. Just pick a ripe, delicious squash or pumpkin, scoop out the seeds, rinse off the orange-yukky bits, and place them on a paper towel to dry. Put in a brown paper bag, label, and store in a cool dry place away from heat.
Cucumbers, zucchini and summer squash, and peppers all need to be "overripe" before you can save the seeds. Grab squashes/cucumbers which have gone feral which have "woody" seeds, those are ripe enough to save. Cucumbers will turn yellow and be mushy and bitter in the middle.
Tomatoes have to be over-ripe and slightly "rotten" before the seeds become viable. Put them in a glass. The viable seeds will sink. The non-viable seeds will float. Scoop out the non-viable ones, This article talks about "fermenting" the seeds, but I never do that. I let the tomatoes which I've selected to save seed rot right on the vine, or take the entire tomato and stick it in a bowl and forget about it for a few days, so I guess it "ferments" right inside the tomato.
https://www.thespruce.com/how-to-save-tomato-seeds-1403292
Other plants should be allowed to "go to seed", such as lettuce, mustard greens, kale, and other plants. Some plants don't go to seed until the second season, at least here in the US northeast where we have cold winters. I select plants for cold-hardiness, so I'll usually select a few plants that displayed hardiness and not rip them up, let them overwinter, go to seed in the spring, and then harvest the seeds. Just snip off the seed heads once they've begun to dry and put them in a cool, dry place to finish drying and allow the seeds to drop out of the seed heads. Snip entire leek or onion flowers and put them on a newspaper or in a brown paper bag until the seeds drop out.