Open a Web browser that has the latest Adobe Flash plugin installed.
Go to MTV's website (see Resources) and click the "Shows" link at the top of the page. Choose "Teen Mom 2" from the list of shows; this will take you to the show's homepage. From there, click the link that says "Full Episodes" on the left side bar. You will be taken to a list of the full episodes that are available for users to watch online.
Choose a "Teen Mom 2" episode by clicking on the appropriate link from your list of choices to start streaming it on your computer.