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).
- Launch quicktime player
- do Screen recording