How to integrate ShopStyle API into WordPress theme?

I’m in a sort of a trouble, so I need some help quick.
The guy I’m working with contracted a job that will require us to integrate the ShopStyle API into the WordPress theme. The example site that i was given, that our final product should resemble is uncrate.com
My guess is that posts with affiliate links need to be created programmatically based on the json or xml feed provided by the api, and beyond this general realization, I’m pretty much clueless about how I am supposed to do this. I never did anything like this before, so I really, really need help.
Can anyone provide some resources or some insight that could help me to figure this out?