Log in to the Manager. Go to Resources->Manage Resources (or Elements->Manage Elements if you’re using 1.0) and open the Templates tag. Edit the template you’re using, and make sure the links to the stylesheets are to your new directory; instead of assets/templates/default/site.css you would want it to say assets/templates/mydefault/site.css
Likewise any other paths to the original assets/templates/default need changing; I can’t think of any others though.
The files in the assets/templates/whatever directories are not the template itself; they are support files like .css stylesheets, background images for the template, stuff like that. The template itself is in the database, and you manage it from the Manager as above. It is simply a plain HTML structure, with the different parts such as the page title, menus and the main content text supplied by MODx tags. That’s why it’s called a template
Don’t feel bad; we all had to start somewhere