Which files/folders from a theme need to be moved

If you wanted to use a theme exactly how it is displayed with the example site, what steps would you need to take in order to get that working correctly? With the assumption you have installed the theme into /themes.

Take example this theme - https://themes.gohugo.io/hugo-universal-theme/

Assuming the exampleSite does not contain any superfluous files (why should it?), you need every file. You need to change config.toml to your liking.

ok so the only files you would be moving would be under “exampleSite”. The
rest of the theme files stay where they are. I thought I read something
about moving the CSS file too?

No. If you rename exampleSite => mySite and put the theme in the correct place, you will have a complete site that is working exactly like the … exampleSite.