To embed a youtube clip, Create a New Post, then scroll through the Blog editor to the Media section and click and drag the YouTube icon into the blog post. You will see the Add a YouTube Video To Your Site video as shown below; just click the < icon in the upper left and then paste in the url of the video you have chosen.
To see how an embedded video looks, take a gander below--but remember you can change how you present the video by clicking on Spacing or Advanced in the YouTube video menu shown above.