In Blogger I just copy the (Embed Code) usually on the right side of the Video on YouTube and paste it into my Post and there it is on my site when I publish it...
Example Code:
<object width="425" height="350"><param name="movie" value="http://www.youtube.com/v/fhtyuejdas"></param><param name="wmode" value="transparent"></param><embed src="http://www.youtube.com/v/sn6ft3btOPE" type="application/x-shockwave-flash" wmode="transparent" width="425" height="350"></embed></object>