The base Zen theme is designed to be easily extended by its sub-themes. You shouldn't modify any of the CSS or PHP files in the zen/ folder; but instead you should create a sub-theme of zen which is located in a folder outside of the root zen/ folder. The examples below assume zen and your sub-theme will be installed in sites/all/themes/, but any valid theme directory is acceptable (read the sites/default/default.settings.php for more info.)
Why? To learn why you shouldn't modify any of the files in the zen/ folder, see http://drupal.org/node/245802
IMPORTANT NOTE *
Copy the STARTERKIT folder out of the zen/ folder and rename it to be your new sub-theme. IMPORTANT: The name of your sub-theme must start with an alphabetic character and can only contain lowercase letters, numbers and underscores.
For example, copy the sites/all/themes/zen/STARTERKIT folder and rename it as sites/all/themes/foo.
Why? Each theme should reside in its own folder. To make it easier to upgrade Zen, sub-themes should reside in a folder separate from the base theme.
In your new sub-theme folder, rename the STARTERKIT.info.txt file to include the name of your new sub-theme and remove the ".txt" extension. Then edit the .info file by editing the name and description field.
For example, rename the foo/STARTERKIT.info file to foo/foo.info. Edit the foo.info file and change "name = Zen Sub-theme Starter Kit" to "name = Foo" and "description = Read..." to "description = A Zen sub-theme".
Why? The .info file describes the basic things about your theme: its name, description, features, template regions, CSS files, and JavaScript files. See the Drupal 7 Theme Guide for more info: http://drupal.org/node/171205
Then, visit your site's Appearance page at admin/appearance to refresh Drupal 7's cache of .info file data.
By default your new sub-theme is using a responsive layout. If you want a fixed layout for your theme, delete the unneeded responsive-sidebars and responsive-sidebars-rtl css/sass files and edit your sub-theme's .info file and replace the reference to responsive-sidebars.css with fixed-width.css.
For example, edit foo/foo.info and change this line: stylesheets[all][] = css/layouts/responsive-sidebars.css to: stylesheets[all][] = css/layouts/fixed-width.css
Why? The "stylesheets" lines in your .info file describe the media type and path to the CSS file you want to include. The format for these lines is: stylesheets[MEDIA][] = path/to/file.css
Alternatively, if you are more familiar with a different CSS layout method, such as GridSetApp or 960.gs, etc., you can replace the "css/layouts/responsive-sidebars.css" line in your .info file with a line pointing at your choice of layout CSS file.
Then, visit your site's Appearance page at admin/appearance to refresh Drupal 7's cache of .info file data.
Edit the template.php and theme-settings.php files in your sub-theme's folder; replace ALL occurrences of "STARTERKIT" with the name of your sub-theme.
For example, edit foo/template.php and foo/theme-settings.php and replace every occurrence of "STARTERKIT" with "foo".
It is recommended to use a text editing application with search and "replace all" functionality.
Log in as an administrator on your Drupal site, go to the Appearance page at admin/appearance and click the "Enable and set default" link next to your new sub-theme.
Optional steps:
Modify the markup in Zen core's template files.
If you decide you want to modify any of the .tpl.php template files in the zen folder, copy them to your sub-theme's folder before making any changes. And then rebuild the theme registry.
For example, copy zen/templates/page.tpl.php to foo/templates/page.tpl.php.
Modify the markup in Drupal's search form.
Copy the search-block-form.tpl.php template file from the modules/search/ folder and place it in your sub-theme's template folder. And then rebuild the theme registry.
You can find a full list of Drupal templates that you can override in the templates/README.txt file or http://drupal.org/node/190815
Why? In Drupal 7 theming, if you want to modify a template included by a module, you should copy the template file from the module's directory to your sub-theme's template directory and then rebuild the theme registry. See the Drupal 7 Theme Guide for more info: http://drupal.org/node/173880
Further extend your sub-theme.
Discover further ways to extend your sub-theme by reading Zen's documentation online at: http://drupal.org/documentation/theme/zen and Drupal 7's Theme Guide online at: http://drupal.org/theme-guide