YOUTUBE, VIMEO EMBEDDING
This is much easier, as the plugin I installed for this function doesn't require codes or tags the way Soundcloud embedding does.
Just copy and paste the URL that appears in your browser's address bar when you're viewing the video on YouTube. Don't use embed code -- it won't work (well, it'll create a clickable link, but the video won't appear inline in the forum, which is the whole point)
This is an example of a valid URL you could insert into a post, and have the video embed automatically. I'll insert the actual URL below so you'll see how it works.