Most seed-savers realize that succulent fruits – like tomatoes and peppers – must be thoroughly ripe for the seed to be viable; however, many do not realize that some fruits – notably squash and pumpkins – will continue to ripen their seeds AFTER harvest, provided they’re kept in the fruit. This is because the fruit, say squash, is in fact a placenta, and the seed continues to draw energy from it even after it has been detached from the mother plant. Therefore, regardless of how mature the seed is at harvest, its quality can improve still further in storage. Understandably, there is a limit to this as the squash will at some point rot and/or the seeds will begin to sprout inside the seed cavity.
Squash/pumpkins will keep best if left to cure in the field for several sunny days, covering against heavy frost or prolonged rain. That way the skin hardens up and any scratches will heal over rather than allow decay to enter. If you then store the mature cured squash in a cool dry place (like attic or shed) it will keep for several weeks, allowing you to eat the squash atb your convenience, removing and drying the seeds from each fruit in turn.
When you cut open the squash to eat or process it, you’ll find each seed fastened to a stringy bit which is essentially an umbilical cord through which it has been drawing nourishment from the mother fruit. This stringy goo will of course need to be removed (both from the seed and the fruit) so the seeds can be placed on a plate or something to dry. Once thoroughly dried, any remaining junk including the dried and flaky goo still clinging to the seed coat, can just be rubbed off and sifted or blown away.
Of course if you’re processing the squash all at once, as for freezing, then you simply have to remove all the seed at the same time, and that’s okay provided the fruit was fully mature when picked; it’s just that this after-ripening will give an extra measure of strength and longevity.
Just a reminder: summer squashes like zucchini are still unripe at the edible stage. They must be allowed to get all overgrown and hard, which of course ruins them for eating (fortunately you only need to let a few go for seed, picking the rest young to keep up production). With most squash however you can have your cake and eat it too.