I found out how to do it.
1) Copy the url from the browser address
2) Click the upload video icon
3) Paste in the url for the youTube video
4) Give it a title
5) Click the insert into post button
http://support.wordpress.com/videos/youtube/
I cannot embed youTube videos either. I pasted the code in the HTML view and when I hit save or update the code just disappears.
