Open Origin.
Press on the Battlefield 3 picture.
A new page will open up in your web browser. It is the Battlelog web page.
From this web page, you can play Co-op, Single Player, or Multiplayer.
Click on Multiplayer (top of the page, yellow icon).
A new page will open up showing you the servers which you can connect to.
Connect to any empty server to begin playing Multiplayer.