This is pretty easy since a fallen blackberry will sprout new plants next spring just by not picking up the berry.

If your soil will remain undisturbed, put a ripe berry at the spot you want a new plant, and thin out the resulting sprouts to one plant.

You can crush a ripe berry and wash the pulp off and save the seeds, but they may require a chill period to sprout when planted next year. Some food mills or juicers may eject the seeds intact.

The quality of fruit from a seedling blackberry may not be as good as the fruit from the original plant. It is much better to get new plants by allowing the growing canes to arch into the ground; they will root at that spot. Late the next winter, cut that rooted cane to about one foot long and a new plant will grow from the base. The ensuing fruit will be identical to the parent plant.

I don't quite understand why you want to save blackberry seed. larry-gene has explained how easy they are to propagate from stems. But they are perennial shrubs and will continue to produce every year for many years. They don't need replanting every year. Just cut out all the canes that fruited this year and tie all the new unfruited canes to your trellis fence or whatever. That's all there is to it. Unless of course you have a big wild type garden in which case just leave them alone.

For tomato seeds, I just remove from tomatoes I like, rinse in a sieve under running water until most of the jelly is washed away. They are then placed on a piece of plastic wrap to dry a week or two. They should be seperated when placed on the plastic wrap. Once dried, I remove from the plastic wrap and seperate any that are still stuck together. They are stored in a paper envelope uver the winter. The next season if I don't use them all, I will place the paper envelop and seeds in a small zipper plastic bag. I suppose you coud do them your way, but if it works well without that soaking in water, why not just dry them.
As to raspberries, no need to save seeds, they sprout new canes every season and don't need seeds to keep them going.

What is the best place to learn how to propagate clippings, not air-layering, but actual clippings? And maybe have pictures to I can see??

well, thank you for the tip on airlayering