This is probably the easiest thing to do in the world. You must first click on the “share” section of your video on youtube.com site and look for a a link or the share button. If youtube goes out of business and I highly doubt that but you can copy the hyperlink and add the iframe before it if another video company comes around. Add that code to your html file or if you are using some kind of CMS system, make sure it is in the html area, NOT the regular text/WYSIWYG because that shit might only appear as code.
Check out this image:
Then Click on the “embed” link,
<iframe src="//www.youtube.com/embed/VIJrZ_VeYYI" width="500" height="300"></iframe>
And finally copy and paste that iframe link over to your “HTML” paste. Not the “Text/Visual” part of the post but the regular “HTML”. Watch the Video for more info about embedding a youtube video in your post.