This can also be done with GIFs. Some GIFs on the internet do not have much movement, and it's usually safe to run those through the reverse image search without more extra work.
However, other GIFs involve a lot more motion, and so it can be trickier (particularly since some of the frames can be useless). This can sometimes be done by "timing" the search right (by clicking just before the right frame) and trying a different points in the GIF, but this isn't very efficient, particularly since it can be hard to get the timing right.
A better tactic is to first break down the GIF into all its frames and search some of the more promising ones. There are a number of websites where this can be done, such as gif-explode. We can then run a couple individual reverse image searches, and some frames might work better than others.
For example, this GIF does very poorly at certain frames, yet as I stated in my answer in this question, some of the frames do work.
Running this through gif-explode, I get the GIF broken down into its frames. (Click on the image to get bigger picture.)
I pick a couple of frames and run them through Google Reverse Image Search, and the frame boxed in red gives me the very useful result of
illya archer, and some links to the Fate series.
Meanwhile, other frames in this GIF give me no result, so it can take a couple of tries.