Roll your cursor over the "watch video" and it will give you viewing options. just click on one of the four listed as streaming with ads and it will play. If you click on the amazon link, you will need to sign up for something.
To watch it on your computer, you will have to type cbs.com on your browser. From there, you should point your cursor at the show hyperlink to be able to select it. You will then select on "Under the Dome" to watch the episodes. Make sure that your browser is updated with flash plug-ins.