In addition to what John says, you might want to look at a library like Colorbox. To see Colorbox in action, visit this page, then click on the "Flash / Video (Iframe/Direct Link To YouTube)" link.
If your video isn't hosted on YouTube or Vimeo, it wouldn't be hard to modify the script to point to a resource on your own server.
Also, Colorbox has various skins you can use. Here's a slightly different one.