Do you wish to post to a category by a visitor of your website? If yes, you will have to go for a complex process. Need to install and activate a compatible plugin etc.
If your categories are not displaying in your blog, then you will have to add proper widgets to your current theme. If you’re a newbie to WordPress, then please go through the page at: http://codex.wordpress.org/New_To_WordPress_-_Where_to_Start and sub pages one by one.