I've been reading that Starcraft 2 has facebook integration. But how do I actually connect my accounts?
If you log onto battle.net, go to your "Home" page by clicking the little house button.
As you can see there, is a button which says "Import Friends" next to the Facebook icon. Select this, and enter in your Facebook credentials.
If the broadcast has expired, select your friends:
Click "add friends":
Select "add Facebook Friends."
As of January 2013, Facebook integration has been removed by Blizzard because Facebook
[...] changed their API usage policy and decided to prevent third-party games like StarCraft II from utilizing their network to make social connections.