The really brief version breaks down into two parts:
1) assuming you have link-posting rights, just paste the full youtube link into your post, and when it gets displayed, the youtube video will automatically display embedded inline in your post. You don't need any special version of the youtube link (i.e. no special embedding code), just copy the url from the page in youtube.
2) every topic has a limit to how many inline youtube thingies it will accept - so once there are too many in the one topic, it'll not display any more beyond that, just show the link for you to click on instead.
So for example, if you just post the link
http://www.youtube.com/watch?v=yUKjh0ey7mc
you'll get this (and who could resist?):
Share and enjoy

.