This is a guide to making smoothly looped GIF, or cinemagraph. The process is a combination of two disciplines: making the loop and making the GIF.
It’s important to note up front that in this guide, both of these steps are accomplished with software in the Adobe Creative Suite. Any prosumer-level-or-better video editing software should be able to make the loop with the logic presented here. I’ll use Photoshop to make the GIF since it’s the most comprehensive tool I’ve seen. Other GIF outputters give less control over similar options, so you might still get something out of checking that section out if you don’t have this software.