MPlayer is a pretty powerful tool for processing video files. It has a built-in command line option that will export specified movie frames to a GIF. Such a feature seems like it would make the guide I'm presenting here obsolete, but the problem with the feature is that the resultant GIF looks terrible: too few colors. As far as I've seen, the best way to get good quality animated GIFs using only free software involves using a combination of MPlayer's command line tools and a little bit of elbow grease in The GIMP.