Okay, serious answer amid all the ribbing: you don't embed Youtube videos on forums unless you're somehow allowed to post HTML code. And then it requires a lot of code and some effort to make it play nice with people's varied browsers. Actually, this goes for any media file that isn't an image already hosted on the web (they're all treated as "objects" according to HTML 5/XML and earlier, while images are just treated as "images").
You can, however, use some scripting tools to allow Youtube links (just the standard URL links) to become embedded into the thread as you read it, and I bet some phones have apps or defaults scripts that do the same thing.
I'm not an expert, I just did a lot of coding way back when the Internet was just beginning to go strong (mid-90's and later). Anyone remember Compuserve chat? Prodigy? Anyway, I got as far as basic PHP, server hosting with Apache, SSIs, basic Javascript, and some slightly more complicated DHTML CSS level shenanigans before I lost interest.