Spun need categories for post, beginner

I a beginner to wordpress, and I love the theme. This is my first time doing a site, and I started not with default them but with the spun theme. So I know that the main page can have 1 page, and as many a post as you can set. So what I want is to have categories on the main page with blogs linking from the categories. So people can find the post better. I will be making a lot of blogs so anything that can organize it will help. I hope that make sense.

Like main page

Each circle as a category on main page, with whatever post I want go to each category.