I have had a look at the Ubuntu Free Culture Showcase Wiki. It has lots of information about how to submit material.
I have no talent whatsoever, however if I see something awesome/spectacular/beautiful, how do I tell the Ubuntu Free Culture Showcase about it?
In short how do I big up my favorite video/picture/music?
Ask The Author
Given the wiki page says that "submission must be submitted by the author of the work", one obvious way to do it would be to ask the original authors to take the time to submit their work. You can send them an email explaining the benefits of having their work be part of the free culture showcase. Like "exposure to millions"[1] of users.
Assuming the licensing is in order, this should give you a good chance at getting your favourite work into the FCS.