1. Select the video on youtube. e.g. https://www.youtube.com/watch?v=nYli9aHqhFI
2. Click on share and then embed.
3. Copy the embed code alongwith <iframe> code tag.
4. Switch to Plain text editor and paste this code.
5. Now switch the text format to Full HTML.
6. If needed, click on preview button on the toolbar of the editor.
7. Now you can see the video.
Note: I have added <iframe> tag as valid tag for "Filtered HTML" text format, but it still does not accept it and does not display the video.