How does post-marking work in the US?

This can vary widely depending on where you live. For example, I live in a major(ish) city, and when I mail something, it gets postmarked right here in some mail sorting room before it goes on a truck or plane to its destination. But, I have family in rural Kentucky, and when they mail me something, the postmark is from the major city that is over an hour away. Before it ever gets postmarked, it must have already been routed through several tiny podunk post offices.

If you go to the counter at the post office you can get stuff postmarked on the spot.