Assuming you want the most robust, free tool for Image editing GIMP. GIMP is available for Windows, Mac and Linux.
Now, if your going to insist on a free open source tool for editing video, options are better on Linux. Are you running Linux? You have about half a dozen options there, but I'm not proficient enough at any of them to make a really good recommendation. I know Kino is fairly popular, that may be a good place to start.
Jahshaka can be used on PC. Not sure hoew adanced it is but I have used it for some basic editing of screen captured video. Seemed ok. Windows movie maker is basic but is ok for cutting and splicing
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Now, if your going to insist on a free open source tool for editing video, options are better on Linux. Are you running Linux? You have about half a dozen options there, but I'm not proficient enough at any of them to make a really good recommendation. I know Kino is fairly popular, that may be a good place to start.