Screencapture and animated gifs
I say "animated gif" but in reality I think it's irresponsible to be serving "real" GIF files to people now. You should be serving gfy's, gifv's, webm, mp4s, whatever. They're a fraction of the filesize making it easier for you to deliver high fidelity, full color animation very quickly, especially on bad mobile connections. (But I suppose if you're just doing this for small audiences (like bug reporting), then LICEcap is a good solution).
cmd-t
.Really, use the iframe. It'll give you better perf and will load way faster for your users.
If you really want a GIF file (terrible), then click the "GIF" icon. It's sweet to let them do the work for us.
However if you want to make the gif on your own.. continue.
Use an app called GIFBrewery but it costs money and is a little weird to configure. But it works. Run it through imageoptim after.
(This path is for people comfortable with homebrew and dotfiles.)
gifify
from @SlexAxton's gist: https://gist.github.com/SlexAxton/4989674 and toss it into your dotfiles somewhrebrew install ffmpeg gifsicle imagemagick
gifify yourvideo.mov --good