Show categories as navigation

Hi! I'm pretty new to Drupal. I tried to search but don't seem to get it (or I don't understand the terms used in Drupal).

My goal is simple: I have created several categories as vocabularies, say Site News, Tutorials, Articles, Reviews.

Now, I want to create a page and group it in Site News to make some website announcements.

Then, I want to write a review on Drupal, and put it under Reviews.

I want these categories to show up on my left sidebar. Whereby when visitor clicks on Site News, they would be able to read my announcement, or on Reviews, they would be able to read the review on Drupal. Each category, when clicked, should list all the associated story.

And, to allow users to categorize their story in the input form also. That means, they can select whether the story they are posting should be grouped to Articles, or Tutorials.

Thank you!