Long ago, Fanpop did briefly have the ability for users to upload videos to the site, but almost nobody used it, so the staff removed it about a month after it was implemented.
So now users should use any video sharing site and then insert the URLs in the "Add a video" form. For more information, you might read the
link.
That said, I would strongly recommend that you use a different video service than YouTube...depending on what you are trying to do. YouTube, now owned by Google, is constantly changing how videos are handled and presented on other sites. In particular, YouTube is terrible for posting videos to pop quiz questions (the answers to the questions are usually in the title of the video, and now YouTube embeds the video title with the video on other sites) and also bad for posting videos involving any content that might be copyrighted (music videos, movie trailers, TV show clips, etc. - YouTube is very quick to remove such content, which then makes for broken links all over Fanpop). So, while you can use YouTube to post your own personal videos, if you want to, say, create a fanvid, I recommend posting it elsewhere, such as on Flickr, Vimeo, or Dailymotion.
