If you're an avid feed consumer like I am, you might be a bit sad to see Google's recent announcement of Reader reaching end of life. Reader was simple and easy to use, but there's no reason you can't have the same functionality with your own homegrown project. The PHP library SimplePie allows for quick and easy feed consumption and display. Here's how you can get started on your own feed reader.
He helps you get it installed (via Composer) and shows you how to use some of its most basic functionality to parse the New York Times' feed. He also includes examples of getting the information back out of the SimplePie object. There's also some snippets that show how to only get the latest items and how to cache the results.