Did you know that spinach has male and female plants? You can't tell the difference until they start to go to seed. (maybe some people can but I can't) This is a female plant. You can see the little lumps in the joints? That is the start of the seeds.
This is the male plant. It gets many tiny flowers all up the stalk. When the plant moves in the wind or if you brush against it, the pollen looks like a yellow dust cloud.
Here is a female plant drying up outside. I let them dry most of the way out in the garden. When you are saving seeds, you don't want to save the first plants that go to seed as that is not a trait you want. You also try to save seed from the largest, nicest plants so you continue those traits.
When the plants are fairly dry, I pull them out of the ground and tie them in bunches. I then hang them upside down in the greenhouse to finish drying. This way I don't have the spinach reseeding itself in the garden.
When the spinach is all dry, I put it in an old chicken feed bag to knock the seeds off. Some people pick the seeds by hand but I don't really care if I have some leaves, etc. in with the seeds. The seeds won't grow any better if they are clean and my way takes much less time.
After crushing the plants to remove the seed, I dump it into a container. I usually spread the seeds out for a final drying. I then sort out some of the larger chaff and then label and store the seeds until next year.