Begin by composing an advanced email. You can access the advanced editor using the blue button to the right on the 'Send An Email' popup that can be accessed from many places in your dashboard
From the content toolbox, drag the video to a content area location.
After dragging the video placeholder into your desired location, click the add a video button to show the content properties panel that will appear on the right hand side, to paste your YouTube or Vimeo URL.
Paste the video URL into the 'Video url' field in the content properties panel.
After the URL is added, click on the video image in the middle to add and reveal some additional options.
There are a bunch of options for changing the style of the play button, and of course your standard padding. However, depending on design, there is an option to hide the video on either the desktop or mobile layouts of the email.