This seems to be a source of frustration with many users, so I thought I'd post this up as a little How-To.
Let's say you want to show this video of 2010 Cleveland Sketch Battle:
http://www.youtube.com/watch?v=EGjVKXQ0xQc
In order to embed the video:
1. Click the "youtube" button above
2. Copy everything after the "=" sign (http://www.youtube.com/watch?v=EGjVKXQ0xQc) and paste that between the YouTube tags [youtube]**right here**[/youtube]
When done correctly, you get this result: