When creating a new thread, the full BBC buttons show up. There is a 'video' icon next to the 'add image' icon.

Just copy the YouTube share url into this 'insert video' dialogue box and click okay.

If you want to add a video reply to someone else's thread, be sure not to use 'quick reply' but instead use 'go advance' (below right side of quick reply text box) so you see the insert video button.

This is also true if you edit an older post where the video isn't showing up. Just copy/paste the video url (starting with http://) as noted above.

Happy posting.