The SitePoint PHP blog has a tutorial posted that shows you how to "conquer" the Instagram API in your PHP application and integrate it into your application with the help of the Guzzle HTTP client.
Instagram’s API allows us to interact with data such as user info, media (photos and videos), likes, comments, and tags. For example, you can search for media around a specific location and filter the results by time. The API also allows us to post comments or like specific media. For now, only uploading media isn’t supported. You can always look at the API endpoints documentation if you want to know about the full functionality.
They start by talking about the two types of API calls (authenticated/unautheticated) and the limits that are included with each. From there the tutorial shows you how to register a new application, get a new client ID and how to use the API console to test out requests. Next they help you get the [Guzzle]((http://guzzle.readthedocs.org/en/latest/) library installed and connect it to the Instagram API with your client credentials. They integrate this into a simple Slim application using Twig as a templating layer to allow for the OAuth approval process, fetching an access token for the later requests.
With the connection made, they show you how to make requests to do thing like make tag searches, get user feed information (and searches), geographic searches and handling pagination. They also include a link to a PHP Instagram library that can help simplify the process, complete with code examples.