Organizing categories

I have categories.I have posts assigned to individual categories depending on relevance.
I am trying to create pages with a category and the posts that go with it.
Example:
I have my “Home Page”.That page contains a link to another page called “Conversations”.The “Conversations” page should have it’s own categories and posts with it.
Then from “Home Page”another link to my next page lets call it “Example 2”.This page has its own categories and posts that go with it.
I hope that is clear enough on what I am trying to do. I set my “Home Page” as a static page but in my dash board can not find out how to link categories to a page and all the posts in that category with it.
My goal is to cover different subjects on separate specialized pages related to each subject all from my home page.
Any help or links to tutorials is appreciated.