Although there is a number of extensions available for Joomla to place a Youtube video within a module position, you will find this is relatively easy to do by simply using Joomlas Custom HTML module.

Before you start I would strongly recommend changing your editor to CodeMirror. Some of the fancier editors will 'clean' your code when saving, removing essentials parts of your code. You will find an option to change your editor to CodeMirror from within Joomla Global Configuration.

1. Grab your embed code from the Youtube video you wish to display. Open your video in Youtube and navigate to Share -> Embed. Select the embed code and copy it to your clipboard.
2. Going back to your Joomla administration navigate to Extensions -> Module Manager -> New -> Custom HTML.
3. Edit your module title and set the module position where you wish your module to appear.
4. In the Custom Output field paste the embed code you have copied from Youtube. At this point you may wish to edit the width and height values of your code to better suit the area of your site in which you wish to place your video.
5. Set your Menu Assignment to the pages where you wish to add your module.
6. Save and your done!