To embed an instagram photo just paste the link to the page into a line in the post:
Get the url for a Vimeo page and paste it in on its own line:
Just paste in a youtube url and the player is embedded.
You can also paste in the embed code from YouTube and it will be converted to a shortcake, this is handy if you want to customise the video size or other options. For example avoid showing released videos.
Alternatively you can add ?rel=0 after the url before pasting it in: https://www.youtube.com/watch?v=u2wrYBPLsxg?rel=0
Which will hide related videos.