So I did get it wrong, sorry for that.
If your calendar doesn't render the classes for its cells, you need to assign a skin to the web part.
Take a look at the example calendar web part's properties, there's a property called Skin ID, with its value set to "EventCalendar" or something like that.
Then view your application files in the file system and navigate to App_Themes/<SiteName> and edit Default.skin. You'll see a code block starting with
<cms:CMSCalendar Runat="server" SkinID="EventCalendar" ...
... which is what you want to add to the skin file of your website.
More info here:
App themes in the Developer's Guide