I'm no novice. However, I can't figure out how to advance to the next turn. The rule book is no help. I spent hours. Clicking every button I can find and trying random keys. I even looked at the key map. It's very frustrating. Something like that should be obvious.

Are you playing the 2022 game, or the old one?

If the original, it's easy to miss how to advance ... you can't as long as you have a unit selected. So finish with every one of your units (hit "done" or "patrol" as appropriate), and then there's a big obvious "next turn" button at the bottom-right (or you can use the "N" key at that point). But it's not there while you have a unit selected.