It's simple, once you know how.
Paste your youtube link into the editor.
Highlight the entire link, then click the chain icon (in the middle, just below "Font family")
Paste the link into the Link URL field, then click Insert. This turns the the link into a clickable link. The forum will automatically convert this into an embedded video after you save your post.
NOTE:The link has to contain youtube.com/watch in it to be converted properly.
Example:
http://www.youtube.com/watch?v=nyTUSe99z6o
Now, an embedded video: