On the youtube.com select and copy the "Embed code" of your desired video
(this code is showing up right next to the video, you're watching.

From your blogs control panel add a new entry to your blog.

Enter a title for your new entry.

Enter (if you like) some more text in the body (what ever you want to tell about the video)

Then hit the enter key twice (to make sure there is a line break, between your text and the video)

Now hit the SOURCE code button of the editor
(it's at the lower right of the tool bar).

This will switch to the html code of your entry.

Just paste the code that you have copied before on youtube.com and press the SOURCE code button again to switch back to WYSIWYG mode
of the editor again.

Now the video should be integrated, but you won't see anything in the editor.

To see if it worked, press the "Preview Entry" button.

Your new entry will show up in an new window, showing how your entry with the video will look like.

If everything is okey, go back to the editor window and press the "Publish on my blog!" button.

Now you're new entry with the integrated video is public!