To embed a YouTube video in your blog.
Navigate to the YouTube video you want to embed. On the right hand side of the video you will see a box with the "Embed" code for that particular video (see below).
Select this code and copy it to the clipboard (press cmd-c on a Mac, ctrl-c on Windows).
On your blog, create a new entry. Select the "Edit HTML" option in the blog edit window (see below).
Paste the code from the YouTube website into the edit window (press cmd-v on a Mac, ctrl-v on Windows).
Note that if you don't select the "Edit HTML" option first, you will most likely just see the raw code on your blog entry (see below)
<object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/R706isyDrqI&hl=en&fs=1"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/R706isyDrqI&hl=en&fs=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object>