1. Install & enable Media (1.4 works fine) and CKEditor.
2. Configure CKEditor:
   1. Go into each profile that should have access.
   2. Go to Editor Appearance.
   3. Make sure “Plugin for inserting images from Drupal media module” is checked.
   4. Remove the Image button from the current toolbar.
   5. Add the Media button to the current toolbar. (It looks like the Image button, but as if the little pictures were stacked!)
   6. Go to Advanced Content Filter.
   7. Add “img[*]” (w/out quotes) to the Extra allowed content box. (Probably you could narrow down the attributes in the brackets, but I’m just going with * for the time being.)

Then: ta-da! It just works. (Assuming that your site has been set up with permissions for uploading via Media module, which is a whole other story.)