I use 2 programs and a website-all free to make them.
First,I grab a video off youtube that I want to make into an animation and copy/paste the URL to this website:
http://keepvid.com/
Just download the High quality version to MyPictures folder.
Now you'll need to screencap it. I use VLC media player which you can download. Open the video in it,get it to the pat you want and push the pause button.At the top,click Video< Snapshot. That takes a picture of the screen.Get doing this untill you've capped the whole part you want-the more caps you make,the smoother and more realistic the animation.
Then I animate them using Gimp,which you can download online. Just open the caps on top of each other (first one you open will be your first image in the animation and so on). Save as a .gif. Click "Save as animation",and "export". Set the speed at 160 (slightly slower works best for some,but thats a good speed to use for most),and Save.
Thats it.:D