There's many ways to skin a cat, but this is how I did it. Make a creative tab, call it "My Video" or whatever. Hard code a link to pcplanets, videocodezone or your favorite video code source, and code it as a popup window. (I put a little flash menu with links to source code that appears only when kids edit their profile.) This way, members can easily fetch video code without leaving your site, which makes for a quick cut and paste.
Now...make sure you are using a wysiwyg editor that will not automatically delete html code when saved. The default editor with joomla will delete code, and while using "no editor" will allow you to keep your code, it is too limiting to run without an editor, esp. to kids who don't know html. Anyway, I use fckeditor and find it works best for my needs. Users just click on "Source", enter their code, and save it.
My site is for young teens who have very little patience with things that take too long or are complicated. However you decide to do this, always remember rule #1 -- KISS.