There are few methods to embed a video in any WordPress blog. We are describing three methods, one by using WordPress plugin, as described by WordPress and another by HTML input.
Embed Youtube video using WordPress plugin
Embedded Video is a plugin for WordPress that allows you to easily insert videos into your posts, integrated from external portals (like YouTube, Google Video and many many others) or they can be uploaded to the web server or a remote server and integrated as well.
Good for those who upload huge amount of videos.
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Embed Youtube video using HMTL
Open the YouTube url you want; click the Share button below the video and then click Embed :

Select the size of video you want, highlight the whole code, copy it, go to HTML editor (of your WordPress post) and paste the code. That is it. Good for those who rarely upload videos.
Note: Save the post after pasting the HTML in HTML mode ( do not switch to Visual mode before saving the draft).
WordPress official method
This method is by simply using code like BBCode. You can find with detailed screenshots here. We guess it does not work for lot of people, as the number of thumbs down (scroll to bottom of that page) is almost double of the number of thumbs up.
Here is the working example, we have used the second method (that is the HTML iframe insertion) :
