Unlike vBulletin or other similar engine which generally require you to wrap a direct link with code, you can just paste the URL direct into the editor window and it will automatically work. There is a button on the toolbar above the editor window that looks like a piece of film, but you don't really need that. The software is smart enough to figure out where the video came from and it will embed it.
Just like that. Copy and paste, done. Now, if you come across any links that are broken on the current site, please let me know! I've ran a couple of scripts to fix the old vBulletin BBcode links, but I'm sure I didn't get them all. Also, direct HTML links got converted over to straight links as well. Let me know about those - just "report" the post. Thanks!