Saving cucumber seeds is easy. Save them from what you would consider overipe fruits - that are yellow. Even using ones starting to dry out or rot is OK as long as the rot has not invaded the seed cavity.
If there is a lot of material on the seeds you can put them through a 'rot' or ferment period, as this will make them easier to separate. I usually add them to a bit of water in a resealable plastic bag or container with a cover, and wait a few days, then wash them, strain them, and dry on non-absorbent plates in a warm and airy place. If you live in a very humid place you may have to dry them in a place that is slightly warmer than ambient temps though don't heat too high or they will die (above 120F or so). You can also use silica gel to help bring down the moisture content. Store in a cool dry place. You can freeze them if dried to between 5 and 7 percent, and they will keep for years. Don't dry on paper or you will have seeds glued to paper. If the seeds are relatively clean you can skip the ferment. However the ferment will increase germination for some cultivars and it can eliminate some pathogens so some seed savers always do this.
However... You can not harvest seeds from cucumbers and expect them to be true, that is, the same as the parents, unless they are: Grown in Isolation and Not Hybrid
Almost all members of the Cucurbitaceae Family are prolific out-crossers. They are also monoecious, having separate male and female flowers on the same plant. Male flowers usually form first, then female flowers. Bees and other pollinators are very important and cross pollinate from plant to plant. Other cultivars (means cultivated variety, the scientific name for what most people call variety, but which botanical taxonomists use in a different manner) of the same species will easily pollinate another, in fact this is often more common given one cultivar may have more male flowers open and another more female flowers open. If this happens a hybrid is produced, but not one that you planned on.
With cucumbers you usually will get fairly edible fruits from the cross, though they will not have the same characteristics as the parents. Sometimes a characteristic that is really negative will come out like completely bitter fruit and these are useless.
So you either must grow them in isolation, which for cukes is 1/2 mile from another cultivar. I've found this excessive, and probably only necessary for commercial growers. But you can't have neighbors with lots of cukes either. You can also hand pollinate (a taping and tagging method is not-so-easy but is possible with cucumbers). Alternate day caging is also possible, but again this will not be possible with neighbors growing them, unless you enlist them into your seed saving endeavor. One of the best resources for this is the book: Seed to Seed: Seed Saving and Growing Techniques for Vegetable Gardeners, 2nd Edition.
Hybrid Seeds: These are from a cross that was planned on. But the offspring of these plants (the seeds) are different from the parent due to independent assortment and recombination of genes. This can result in really surprising fruits - especially if one of the parents was close to a wild type plant. You might be really hard rinds, huge or tiny seed cavities, Strange growth patterns, etc. They are usually edible, but occasionally this is even a problem, and you only get really bitter fruits. That being said, some so-called hybrid seed is not really hybrid, or at least from parents that are not that different, and the offspring of these will be very like the parents. But you won't know this from the seed package. You have to wait out the year to see, and even save from year to year, and not many people have the time or space to do this.