Every site is different and some don't even offer oEmbed. A ton of work has gone into embedly. You can repeat the effort, and host your own solution, or just use us. We think using Embedly is a cheaper solution.
i believe reddit uses them:
1. a user creates a new post with a link that goes on youtube/vimeo/whatever
2. use embedly api to extract the video/thumbnail and show it in your site. At reddit there is a |> button to press and u can see the video.
For example check this page: http://www.reddit.com/r/videos/