Animated GIF images have are very popular on the web, as you may have noticed. You can create animated GIFs quite simply with a collection of photographs. Most phone cameras will have built in methods so you don’t even have to think about it. There are some online applications too that allow you to upload your images and share the completed animation in a variety of ways.
The HTC one, for example, has a couple of ways to create animated gifs. The camera has a Zoe mode where the camera takes multiple shots in quick succession. It stores them in the gallery like all your other photos. The other useful thing about the Zoe effect is that if you just want a single image, you can edit the animation, select the best shot of the range; so you can always get your best side!
If you’re not too keen on creating them manually (or simply don't know how), you can download one of the many useful free apps to simplify the process and save time. About Technology have a list of 9 free GIF maker apps you can get started with, on your iPhone and/or Android.