If you want to embed or insert a youtube video into a WordPress page it is super easy. Just grab the link to the video…
Paste that into the WordPress page and you’re done.
The following screen capture demonstrates the process.
There is one common error that you might experience which is if the text is a hyperlink, eg. it is blue with an underline it won’t substitute for the video when you view the website. If the text is a hyperlink highlight the text and use the unlink menu button.
There is a detailed explanation of the embedding options here: http://en.support.wordpress.com/videos/youtube/