Embedding YouTube videos into Moodle is actually fairly easy.  YouTube is helpful enough to actually provide people with the embed code for all of their videos, so you don't actually need to know how to use HTML code to embed videos. 

The first step is to find a video on YouTube you want to put on your page.  When you have the video playing, on the right under the description of the video are two textboxes named URL and Embed.  Click in the Embed box, choose Select All, and then Copy from the Edit menu.

Next, go to your Moodle page.  Either Insert a Label on your main page, or Compose a Web Page if you don't want the video on your main page (in which case, the only difference in the next steps is that you need a title).

• In the text box where you normally type, enter any notes about the video you may want to have appear above the video. 
• Then, click on the button called Toggle HTML Source.  It looks like this:  <>
• After the text you entered, there will be a <br />   (this represents a carriage return).  Put your cursor to the right of that, and the Paste the Embed code you copied from YouTube.
  
• Save your page or label, and you are all set!