Adding Categories via the Dashboard > http://en.support.wordpress.com/posts/categories/#adding-categories-via-the-dashboard
Adding Categories to Posts via the Categories Module > http://en.support.wordpress.com/posts/categories/

A custom menu allows you to display Categories with drop-downs to sub-categories in tabs along the horizontal navigation where normally only Pages tabs are displayed. If you wish you can also include Pages with drop-downs to sub-pages and/or Tags pages and/or Custom Links in your custom menu as well. You are in charge of what appears in a custom menu. You choose the order in which to display any and/or all the foregoing in your custom menu. You choose which to display and which to hide.

Creating a custom menu > http://en.support.wordpress.com/menus/
Adding Categories pages to a custom menu > http://en.support.wordpress.com/menus/#adding-category-pages-to-your-menu

Here’s a link to a custom menu walkthrough > http://onecoolsitebloggingtips.com/2011/08/11/wordpress-com-custom-menu-walk-through/

There are many common errors, misunderstanding and misconceptions when creating custom menus and you can read about them here > http://wpbtips.wordpress.com/2011/12/19/custom-menus/

The support documentation is found at the Support link http://en.support.wordpress.com and the searchbox there provides results from both the docs and from forum threads.