Select Source from the Rich Text Editor toolbar. This displays the HTML code for the text box.
Position your cursor where you would like the video embedded, then paste the YouTube embed code (Ctrl + V for PC or Command + V for MAC). The embed code from the video is highlighted for emphasis.
This returns the text box display to normal editing mode. The embedded YouTube video will display as a box marked "IFRAME". When the item using the text box is posted or saved, it displays the embedded YouTube video.