Firstly, you will notice that the board has a new button icon on the BBCode box
Posting a YouTube video:
All the videos have it's own ID, you can find the ID in the URL of a video. Look at this URL for an example.
6B26asyGKDo is the ID of this YouTube video.
So click on the YouTube button which will place the tags in your post [youtube][/youtube], now all you do is copy the ID of the video from the URL (highlighted above in red) and place it between those 2 tags, and then post.
Enjoy posting videos!