On the main page, click “Launch”. A new brower window opens Ignore the egregious UI-design, and click on any show to rotate it to the front. Click on the show again to launch Play mode. Click the Play button.
If your connection speed is less that 500kbps, you’ll get a “Your View Experience May Suck Because You’ve Got A Crap Internet Connection” message. (aka “Your viewing experience may be less than optimal because your bandwidth appears to be below 500Kbps. Click on the close button to remove this message.) Click on the X to close the message and proceed with playback.
With luck, you’ll start to watch. Without luck, you may have to keep clicking around until playback starts. And you’ll probably run into a few commercials along the way.
Update: Outside the US? Look here for info about watching from abroad.