I'm sure there's an easier way.
I download a video, if needed I convert it to a format I can edit with Windows Movie Maker. (It came with the computer). Once I have a clip I like, I put it on my Android tablet and convert it to a GIF with more free software. I save them to either Skydrive or Dropbox. (More freebies!) It's a pain but it only needs internet for the initial video download and finished upload. Some of the other sites retain your files after you make them. Mine stay mine until I share them.
I'll put a couple up tomorrow.
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