When you use the Facebook icon on YouTube that will post the link as a post on your Wall, you won’t be able to add it directly to your friend’s post that way.
When you click share it displays new content on the screen including a URL for the video. It should already be selected (highlighted) so you want to copy that URL to your clipboard.
To do that, right click on the URL and select Copy or just press Control-C on your keyboard (this assumes you’re on a Windows machine, if a Mac the keyboard command is different).
Now go to your friend’s post on Facebook and paste that URL into the comment box (right click and select Paste or Control-P when the cursor is in the comment box).
If you want to paste it into a comment, the best thing is to copy the link from your browser address bar, and then paste it into the comment space in facebook. Facebook will then parse it as a video.