Video is hard, because there are many formats, but no one format is supported on all browsers. There are different ways to include multi-media with a web page:
Embeding a video from YouTube.com is the easiest way. If you find the video on YouTube.com, you can just include a link to it. Most YouTube videos are available in multiple formats, and will send one to your browser, that your browser can display:
Using the new HTML5 VIDEO tag, you can display video on your computer, and offer it in multiple formats. The first one a browser understands will be used. If the browser doesn't understand the HTML5 video tag, then the OBJECT tag will be used instead, with the EMBED tag as a final fall-back:
(Video downloaded from camendesign.com/code/video_for_everybody/test.html.)
Of course, this solution required you to have your video available in several formats.
Flash is easy, just use the EMBED tag. But won't play on Apple devices such as Macintosh or iPad (You can't usually control if it auto-plays or not, either):