Unlike making a cinemagraph, there are dozens of softwares you can use to make GIFs. The most important thing is to have your photos/videos edited before attempting to make a GIF. This includes making sure your photos are the same size and orientation. However, many softwares include editing of the final GIF, such as color tints or stickers.
One of the best go-to GIF makers is Giphy, an online archive of millions of GIFs. Giphy can create GIFs out of photos, other gifs, and videos. I have also used ezgif.com to
If neither of these programs are what you are looking for, lists of other websites that can create GIFs are located here and here.
Just like with cinemagraphs, Photoshop can also make GIFs out of artwork, photos, and video. Again, if you aren’t comfortable editing in Photoshop, just make sure to have your content edited beforehand.
This is a tutorial on making GIFs out of drawn digital artwork:
This is a tutorial on making GIFs out of photos:
And finally, a tutorial on making GIFs out of video:
IB Digital Art Resources 