In my years as a fur, and in running furry forums, one of my biggest personal frustrations stems from furries attempting to introduce the fandom to non-furs in their lives (parents, family, friends, partners, etc), and completely failing at it. I can't count the number of times I've attempted to point this out just in threads on one website, not to mention when the subject comes up on LJ, IM conversations, and places like the Anthrocon forums.
Now, my public relations skills aren't that much more adept than others, and when I was new, I made many of the same mistakes in introducing the fandom to others. But, since then, I've been to public/media relations panels held by Uncle Kage, and learned a lot from them. If you're ever at a con where Kage hosts one of these panels, I highly recommend attending; not only is he a gifted orater, but he really knows his stuff and has a lot of experience in dealing with the media. But, not everyone can make it to furry cons, and even fewer people have the patience to read the wall o' text on his website that he's written on the subject.
Thankfully, someone at Anthrocon was gracious enough to record the panel and put it on Youtube. This is the entirety of the panel, a full hour long, but it will be the most informative (and entertaining) hour of video you'll ever watch. So, if anyone reading this ever considers telling anyone they know about the furry fandom, please watch these videos first.
This video series was recorded at Anthrocon 2009, from the "Presenting Furry Fandom To The Public" panel led by Uncle Kage. Kage, aka Dr. Samuel Conway, has been the chairman of Anthrocon for over a decade, and is a renowned comedian in the fandom. In addition to a distinguished career as a chemist, he's also had extensive media relations and public speaking experience.
Additionally, Anthrocon has a great "About Furry" page on their website, including a printable brochure that can be given to parents, friends, or other furs. Check it out here