To help developers get started, Apple created an example app using the Photos Framework. Further, Apple provided a Live Photo editing video instructional originally presented at WWDC 2016. SDKs that support Live Photos are within Xcode.
Apple's latest API is not the first move towards integrating Apple Live Photos with third party apps. Tumblr began supporting Apple Live Photos last year. While Tumblr included a somewhat hacked together tool to help developers embed Live Photos, Apple now bypasses the need for such developer gymnastics with an API direct to Live Photos and associated editing tools. Checkout the Live Photos for Developers site to learn more.