You can copy the /bartik/css folder over to your subtheme
> /sites/all/themes/yoursubtheme/ so you can override core theming
> using
> the correct terminology.

> Now the trap you will run into is:
> When you update Drupal core, it updates the core bartik theme which
> calls on a lot of core includes and this can break your
> bartiksubtheme.
> Been there, done that.

> Hope this helps

This is certainly the clearest explanation of how to create a sub-theme, but it confuses me. I'm lead to believe that it is not necessary to reproduce all of the contents of the base theme in the directory of the sub-theme; the point is to inherit all of this so you also inherit updates. If I read this correctly ( https://drupal.org/node/225125 ) I don't need to provide anything but at least one new stylesheet; everything is inherited from the base theme. 

Thanks for the help, 

Chris.
You are partially correct.
Understand just what you are inheriting, is the best advice I can offer to you.

Unfortunately there is no easy way to theme Drupal.  It is a big, complex, messy, time consuming  undertaking.
As a hint, have a look at say Garland, Mayo, Danland theme code and get a feel for the depth of understanding needed. Mayo is a great study case in complexity.

There are hundreds of theme styles and if you look closely they are virtually variations of the same theme,  they just do things differently but still call core functionality.

Every theme inherits most of it's functionality from core, that's the basis of Drupal. But you will want to tweak, this is a given. And that is where you need to copy out the bits you wish to manipulate. Golly we are only talking about half a dozen or so files, not the whole system.

There is no need to reproduce all of the contents but you do have to have your own templates in your sub directory. It's a safety precaution.

Mind you this is only a short cut, an easy way in to a quite substantial development cycle, otherwise you will have to re do it all bit by bit manually and wind up with much the same.

Bartik as with the other core themes has calls to the includes folder and you will also have to copy some of those out as you need them to your sub directory so that you can over ride them as needed. Don't go there until you are comfortable with how the theming works.
HTH
Roger