How do I use the function theme() to create a Menu?

Well, everytime I use google to search for my issue all I get are links and links telling me how to start creating a Drupal Theme but not how to handle this function.

Drupal site tells how this function works. But does not tell you how to create a 'theme' (HTML code to be called from the function theme). I hope I make myself clear, I have to use the word theme for different subjects.

What I mean, I want to create a theme called "links", so that I can call it with the function theme() in this way: theme('links'). How do I do that?

And then... The menu I want to create with simple html stuff is thrown to the screen.