Various Index Post Sizes

I have seen WordPress websites who use various image sizes on the front page.
For example, in my theme, a large MOST RECENT image is shown and then smaller OLDER article images are shown after.

How do I get a third and fourth size etc?

I want the most recent article to have its own layout.
I want the remaining articles to generally have another layout.
But I want at least one more article layout in that stream of most recent articles to be shown on index.php