Pause all notifications
If you want to temporarily stop notifications appearing, the easiest way is to simply hold down the Option (alt) key and click on the notification center icon in the top right corner of the screen. It should become greyed out, indicating that notification center is turned off. Alternatively, while viewing your notifications, scroll up to see a switch that will allow you to pause notifications for the rest of the day. This is great as a “do not disturb” setting - for example if you are watching a movie or giving a presentation.
Access notifications using a gesture
The swipe gesture used to access notification center is a little tricky to get the hang of at first. It’s a two finger swipe from the right towards the left of your trackpad. The best way to do this is to start with your fingers actually off the right side of the trackpad, then swipe left onto the trackpad. Swiping back in the other direction hides notification center again.
Add a keyboard shortcut
If you don’t have a multitouch trackpad, you can just click the notification center button in the top right to see your notifications. But to speed things up, you might want to add a keyboard shortcut. Just go to System Preferences, and in the Keyboard section click the Keyboard Shortcuts tab and find Show Notification Center under Mission Control. Enable the shortcut by ticking the checkbox, then press whatever shortcut you want to use.
After upgrading to Mountain Lion, when you first visit Twitter in Safari and log in you will be asked if you want to allow other applications to access your account. Alternatively, you can manually add your Twitter account(s) by going to the Mail, Contacts & Calendars section of System Preferences. Once an account is set up, a Click to Tweet button appears in notification center, allowing you to quickly send tweets without first opening Safari or a Twitter app.
There’s no Facebook integration yet, but according to Apple it is “coming this fall.”
Disable notification sound
By default, every notification makes an alert sound as it appears. This seems fine at the moment, but I have a feeling it will start to get annoying, especially with apps like Messages. Fortunately, in the Notifications section of System Preferences you can specify which notifications can make an alert sound on an app-by-app basis. Just un-tick the Play sound when receiving notifications checkbox.
Banners vs. Alerts
Also in the Notifications section of System Preferences, you can specific whether notifications for each app appear as Banners or Alerts. Banners are most like Growl and iOS — they appear in the top right and fade out automatically. Alerts will stay until you click the Close button, and also sometimes have extra options, such as a Reply button for message notifications.