I finally figured this out: See http://drupal.org/node/1434814#comment-5583354 for the solution. The most important bits are:
If you're just using the basic CKEditor module, ckeditor.config.js is completely irrelevant to getting your toolbar set up. Ignore it.
CKEditor toolbars are associated with text formats, like "Filtered HTML" or "Full HTML" (or, presumably, other text formats you might define). Each text format can be connected to exactly one toolbar; when a textbox with that text format appears, its toolbar will be presented.
