To claim your free shirt, simply log into Xbox live, click on the Mists of Pandaria advertisement and watch the trailer. Once it's finished, you can click on the "Free Avatar Gear" button to pick the shirt of your choice. Ads on the Xbox Live dashboard are usually random, but the Mists of Pandaria ad will be available on the Home screen all day today.
An alert reader pointed out that if you can't make up your mind between shirts, you can press B to go back and get the other shirt, so you can have both in your collection. Don't waste any time, though -- the promotion ends October 6, 2012.