Photoshop has a command called "Import Video Frames to Layers" which you can use to create animated GIFs. It's a bit complicated but it also gives you the ability to edit GIFs, add captions, and do color correction and other such things.

For a good tutorial on the use of this function see: http://www.wikihow.com/Make-an-Animated-GIF-from-a-Video-in-Photoshop-CS5

This command supports certain formats but not MKV, which is probably going to be your source material format, so you need to convert it. A great free converter is Handbrake and you'll want to export in MP4. http://handbrake.fr/

When you use "Import Video Frames to Layers" you choose the segment you want with a slide bar similar to the methods described above using Virtual Dub, but it isn't that great to work with and besides, converting an entire episode or movie for one small segment takes long and is just annoying. For that purpose you should get the SolveigMM AVI Trimmer + MKV which enables you to very accurately snip a tiny portion out of any MKV (including 10-bit) in a couple of seconds, which then shortens your conversion time substantially. http://www.solveigmm.com/en/products/avi-trimmer-mkv/

The Photoshop method is definitely more advanced but if you spend some time tinkering with it you can do all sorts of really cool things.