FOR YOUTUBE: Just paste the URL into the editing window. Works with both visual and HTML tab.
(2016 update: This video is a little dated. No more Twitter for news site)
FOR VIMEO: Click on the the little paper airplane icon in the upper right hand corner of the Vimeo file for the embed code. Select the “HTML” or “Text” tab on the right of your editing window and paste it in.
Looks like this:
Insert it in the WP editing window under the “Text” tab in the upper right.
Here’s what you get:
On a lighter note: