auxclass has provided you with a link to instructions for adding Categories to your posts. My comment here is focused on display of your Categories in the horizontal menu of your blog.
Staff have provided this support documentation entry for those who want to structure their blog like a website which is what you want to do. > http://en.support.wordpress.com/using-wordpress-to-create-a-website/
What’s critical is to understand when creating a website structure is the following:
1. The differences between pages and posts > http://en.support.wordpress.com/post-vs-page/
2. There is only one dynamic page in a blog for posts and we cannot post to more than that one page. When we publish a post it automatically appears on the running page for post and also on the Categories pages and Archives pages.
3. We organize our posts by assigning Categories to them. Although there is only one dynamic page in a blog for posts and we cannot post to more than that one page, we can create the appearance we have done so by creating a custom menu. In that custom menu displaying Categories in tabs along the horizontal navigation to achieve what you want.
These are the ho-to instructions:
1. You create a custom menu. http://en.support.wordpress.com/menus/
2. You add the Categories you want to display and arrange them in the order you want.
3. Then you add and drop and drag the sub-categories below the appropriate Categories, and when you have everything arranged in the menu that you want you save the menu.
4. Go to the “theme location” module at upper left on the menu page. Select your custom menu name from the pull-down labeled “primary location.” Click the save button in that module.
5. Refresh your browser so that it isn’t possibly pulling a cached page, and view see your new menu with Categories and drop-downs to sub-categories.