You can activate your Game Key on Origin either online, or by downloading the Origin client for PC.
In case you use the online sign in, click on 'My Game Library', select 'ADD A GAME' option and click on 'Redeem Product Code'.
In case you use the Origin Client for PC, instead of 'My Game Library' you will need to select 'Origin' from the top Menu, then click on 'Redeem Product Code'.
Now simply enter your game key in the 'Enter Product Code' field and click 'Next'. Please make sure that there are no spaces before or after your code.