Go to: http://www.origin.com/us/about
Click "Download Origin" (from the upper left corner)

Login into downloaded application
Install and start application, login with your Account name and Password
(create one here: http://store.origin.com/ if you don't have).

Redeem Product Code
From the "Origin" drop-down menu (upper right corner) choose "Redeem Product Code…",
enter your code and click "Next".

Download your Game
After successful code verification go to the "MY GAMES" tab and start downloading.