There's a great new feature in the latest weekly version of Moodle (and
in the forthcoming 1.9.6 release) that enables course designers to
easily embed videos for YouTube.

With older versions it's necessary to paste in the code from YouTube
which can be daunting and students who attempt this have the code
stripped out on saving e.g. a forum post to safeguard against the
potential security risks associated with introducing code in this way.

From now on it's easy for all users to embed YouTube video by using the
in-built multimedia plugin.

1. The first step is for the site administrator to upgrade your site.
2. Enable the YouTube option.
3. Find the YouTube video you want embed and copy the URL.
4. Find the place where you want to embed the video and open it for editing.
5. The following works with the HTML editor enabled, type in some text
and select it.
6. Click on the Insert Web Link icon on the toolbar.
7. Paste in the URL from YouTube into the URL field in the pop up and
click "OK"
8. The text you typed in should now be a link.
9. Save the page and the video is safely and neatly embedded.

That's it!