Here is a video tutorial of the process shown in this article. The screens are different.
Written Tutorial with screenshots
Choose the desired YouTube Video.
Not all videos may be embedded. If the embed code is unavailable a link may be provided or an alternative video may be selected.
Copy the embed code.
There are additional options, but the default options are sufficient.
Embed Code sample. This is called an iframe. <iframe width="560" height="315" src="https://www.youtube.com/embed/Dj0oCiea1ro" frameborder="0" allowfullscreen></iframe>
This code has been used to embed the video below.
Open your course page and choose the desired content block for embedding the video.
Change the width="" and Height="" to fit the embed into your content. Change width to width="100%" while the height may vary depending on where the embed is placed. Start with height="150" click OK and take a look. Adjust the height until you are happy with how it appears on the page.