How do you use other libraries without Mix?

I have no desire to duplicate Mix, I just want to understand how things work behind the scenes, starting from basics. For instance I have started a small Elixir project - Help with choosing data structures for template project - #5 by vonH, all that source code is in a file named templates.ex.

If I want to start a mix project around the modules in that, how would I go about it? Mix does a lot of magic in the background but I need some knowledge of how Elixir programs are structured. I understand that Elixir works around the concept of the module, but what is going on when mix compiles them and ties them up together?

If you look at the mix page on hexdocs, you see only the skeleton. It doesn’t show how the actually working modules is integrated to it. In the application function there is a list such as

def application do
  [mod: {MyApp, []}]
end

There is no real clarity as to how the code in templates.ex I want to use end up integrated in the mod area or how I can even access them in iex.