I've seen several references to 'Compiz Config' and a 'gnome config' application that seems to not be installed by default. Where do these config applications store their data? Is there a registry similar to Windows or are there just some files that I could edit by hand, if I really, really wanted to?
The 3 most common applications you will hear about when talking about tweaking Gnome/Unity will be gconf-editor, dconf-editor and ccsm.
You can find those in the Software Center and install them from there.
The 2 first tools will configure different (sometimes not so different, think of it as a path that leads to the same goal) aspects of your Gnome configuration and the last one is important to configure your Unity/Compiz configuration.
gconf-editor stores its data in XML files in /etc/gconf/
dconf-editor uses files called key files stored in /etc/dconf/db/
ccsm stores its data in XML files in your ~/.gconf/apps/compiz and ~/.gconf/apps/compizconfig folders.
Any of these can be read and edited with a plain text editor (nano, gedit, etc.), but it sure is a lot of work. Use the appropriate tools to edit those files, and it will make your life much simpler.
