Facebook has linked accounts, where facebook logs you into facebook everytime you are logged in with your google account.
So if you're logged in into gmail then visit facebook.com, facebook will automatically log you in!
How do you do this for your own domain so that when a user visits your website it logs you in into your domain? (Does facebook use google open id for this? If not, what does it use?)
That is a rather open-ended question. Here are some links to get you started:
You probably want to look into Open ID technology. Google also offers a single-sign on API that you should look into.
One of the lesser-used features of OpenID is the command to return immediately. Facebook directs you to the Google OpenID login page, with the "reply immediate" command set. This means that Google immediately replies with either your login credentials (just like a normal OpenID login) or with nothing (unlike a normal OpenID login, which would leave you looking at the Google login screen). In that case, Facebook present you with their own login screen.
Facebook do this with a couple of major OpenID providers and thereby claim to have implemented OpenID login.
I picked this up in various reading of various blogs, and wrote it off the top of my head. A quick Google search finds this page, which has some information on the topic: http://openidforum.com/index.php?topic=3.