(Quick-and-dirty excerpt from a post on Community, to make this information persistent and accessible.)

…we have players that can be embedded directly in the post, which is not only convenient for the reader, they don’t autoplay, and are generally small and polite. When you see the little YouTube video, stopped, right in the post, there’s no confusion that you’re being offered a video.

You set them up with simple codes inside square brackets. Because square brackets have special meaning and WordPress often chokes on them, I’ll use {squirrely braces} instead. But substitute [square brackets] (which I bet will work because “square” is not a widget).

There’s a YouTube video player which is braindead simple to use: {youtube id="kYxqTrLz1qY" /}

The “id” part you can copy from the video’s page URL, e.g. : http://www.youtube.com/watch?v=kYxqTrLz1qY

If you’re not sure which part of the URL to use, include the whole URL and my script will figure it out: {youtube}http://www.youtube.com/watch?v=kYxqTrLz1qY{/youtube}.

The default player is a tiny 320×240. You can put in 'width=""' and 'height=""' attributes in the code to specify something else.

The MP3 player follows a similar pattern: {mp3 url="mp3_url" /} or {mp3}mp3_url{/mp3}

There are several other kinds of players available, for the more obscure media types. Too many to document right now, but if you need to play video or audio of another type, please let me know.