Help with custom menu

Hi

I am trying to create a wordpress theme, but are having some trouble

I am trying to create a sidemenu that looks like the one on this page:
https://designduck.dk/glh/udstillinger-program.html

But I have no idea how to, so at the moment I got nothing:
https://designduck.dk/wordpress/udstillinger-program/

I need a menu that I can change for the subsites. So if you go to “Bes?g Gl Holtegaard” instead, it’ll show a different menu.

Any ideas?