How to override subtheme settings (inheritance)?
Assuming you've cleared the cache and all that before trying to inspect any changes, it sounds like your base theme (the theme you've based your sub-theme on) is one of those themes where the configuration is for a large part done by means of the administrative interface. This means that edits done to the .css fileshave no effect, as they're overridden by settings the administrative interface.

A number of popular themes has this property, including the Adaptive Themes family and Omega 3.

To check out if this is the case, navigate to Administration » Appearance » Settings for your theme (or sub-theme).  If there is a lot of settings for fonts, etc., hacking the .css files will not help much and you need to use the administrative interface for styling.