I just upgraded my MacBook Pro from Lion to Mountain Lion.  I read about the new notifications center feature and wanted to add my Twitter account so I can get Twitter notifications.  However, after clicking on the notifications center icon and also looking at  system preferences – notification settings, I could not determine where you add your Twitter account.  After some more poking around I finally found it.  Its under “Mail, Contacts & Calendars” system preference.  Not every intuitive.

Mac Preferences

Once you click on the “Mail, Contacts and Calendars” icon, a new screen pops up that shows your existing mail, calendar and other accounts.  To add Twitter, click on the plus icon on the bottom left side of the screen.  Next, click on the Twitter logo on the right side of the screen.  You then will be asked to supply your Twitter username and password.  Once you signin, the notification center will then receive Twitter notifications.