Extract data from a website API and display content on WordPress.

I've been given some url's which point to data that needs to be pulled into a WordPress site I have built. Not much else information has been provided apart from the url's and how the data needs to be styled.

I need someone with API and WordPress knowledge to extract and display this API data on the website in a way that will let me apply css to it for formatting purposes.

I have the HTML mock-up of how the data should look and be displayed.

The website is all built. I just need this API work to be done.