This is a checklist for creating cinemagraphs with Adobe Photoshop.

1. Create a video file from the section you want to use. The section should loops seamlessly or can be reverse looped without looking stupid.
2. Import video frames.

   File > Import > Video Frames to Layers.
       X From Beginning To End
       X Make Frame Animation
   Move all images under one group, except the first frame.
   Add a clipping mask on the group, outline only the section that changes.
   Open "Animation" windows and see how it looks.
   

3. Optionally create a reverse loop.

   Copy frames in the "Animation" window
   Paste them in the end.
   Right Click > Reverse Frames
   If the reverse looping looks fake, change the delays of individual frames.
   

4. Optionally limit color palette to 256 colors for GIF.

   Add Color Balance adjustment layer on top of the layers to unify shades.
       Turn off Preserve Luminosity.
   Add a Gradient Map adjustment layer.
       Add a gradient from #020413 > #a8c6a0 > #feffe6.
       Change layer style to Lighten.
   Add a Curves adjustment layer.
       Increase contrast to reduce color shades from the image.
   

5. Save the cinemagraph as a GIF or video.

   File > Save for Web > GIF.
   

Sources

• How To Make a Cool Cinemagraph Image in Photoshop