There are two places you can add a YouTube video in your stories.

The first is as inline media in any text column, available in the Text, Background Scrollmation and Scrollmation sections. Between each paragraph break you'll see a media button:

Click the media button to edit. You'll then see four options: Image, Video YouTube and SoundCloud. Click YouTube:

Once selected, you'll be asked you to enter the YouTube video URL. You can also add an optional caption:

Once you've entered the relevant information, simply save the changes and it will take you back to the text column view with your video inserted inline.

The second place you can add a YouTube video is within the Media section. Once you've added this section to your story, you'll see the default image of a Robin. Select the media icon on the left hand side of the image to add your video:

You'll then be able to edit the media. This time you'll see three options: Image, Video and YouTube. Click the YouTube option and add the URL in the same way.

Save your changes, you'll then be taken back to the main editor view and your video will have been added: