don't ask me how it knows which user and password to use to login, it just seems to work somehow ..
Contacts
install Google Contacts addon
if it does not automatically detect your gmail account from the email settings add it manually:
in the addons manager find this addon and click on Preferences
add your account(s) and click ok
you may need to restart thunderbird to see the new addressbook
if you have access to other people's addressbooks i.e. through google apps for businesses, it will automatically show your and all shared addressbooks you have access to once you set up your account.