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 shortcode, this is handy if you want to customise the video size or other options. For example avoid showing related 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.
Or https://www.youtube.com/watch?v=NMmwxn7XBkw&w=600&h=600rel=0 which allows you to control the dimensions.
If you are wanting to do more than embed one or two videos you might find the Embed Plus for YouTube plugin handy.