How to create category 'cloud'?

Hi!

I would like to make it possible for my readers to choose which category of blog posts they’re seeing. E.g. if they want to see blog posts about ‘productivity’, ONLY blog posts referenced as such will show up in the feed below.

An example of what I’m talking about can be found on Nat Eliason’s article page.

On his page, you’re as a reader able to choose which articles show up in the feed below based on which category you choose. The url doesn’t change, which means you aren’t pushed to a new page. The feed below simply changes.

I want to “steal” this design and implement it on my own blog. How on earth does he do this?