If a movie file is not streamed, then the file just gets tossed into your browser's cache. You just have to find it and (in Firefox) put the right extension on it, since Firefox cache files don't have any extensions. Set a bookmark for the page with the video, clear out your browser cache, revisit the page and watch the video, and then look in the browser cache for the biggest file.
Otherwise--
If they are streamed (or in some other video format that is set to prevent regular saving) then you need screen-recorder software.
AutoScreenRecorder is the name of one that has a free version.
Some others are Streambox, Hypercam and Fraps.
Often you need to mess with your computer's video settings to get them to work, else you just get a black rectangle where the video should have been. The FAQ pages for the programs usually explain this in detail.
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