How to add custom css files in a theme from drupal.org?
While you can add your own styles to the Zen theme, it would require that you hack the theme.

What you should do instead when using Zen, is to use it as a base theme, and create what's call a subtheme. That is a theme that will use the styles, templates etc from the Zen theme, but where you can custom overrides, alterations and additions without changing Zen itself.

There is a detailed handbook page where you can read about how this is done and what to be aware of.

Within the Zen theme there is also located a start kit for your subtheme that will help you to do most of what needs to be done, and documentation on what to do in the README file in the theme.