Notification Center is a welcomed new feature in OS X Mountain Lion, replicating the Notification Center in iOS, and replacing third party solution such as Growl.
Shortcuts to display Notification Center
To view the Notification Center with the list of notifications, click on the Notification Center icon at the far right of the menu bar. A narrow band with the list of notifications will slide out from the right of the screen.
By default there is no keyboard shortcut to display the Notification Center. You can setup one from System Preferences>Keyboard. Select Keyboard Shortcuts tab and click on the checkbox for “Show Notification Center” and type your key combination as the shortcuts.
To display the Notification Center using the trackpad, simply swipe from right edge of the trackpad to the left with two fingers.
Notification Center as Hot Corner
Notification Center is available as an option for Hot Corners. The setup is under System Preferences > Mission Control on the left-bottom “Hot Corners…” button. Notification Center will display when the cursor is over the configured corner.
Switch off notifications for a day
If you need some peace and quiet moments, you can switch off incoming notifications for a day. The “Show Alerts and Banners” switch is hidden by default at the top of the Notification Center. Use Option-Up Arrow keys or swipe down with two fingers on the trackpad to display the switch.
A quick way to disable incoming notifications is to Option-click on the Notification Center icon on the menu bar. The icon will dim slightly indicating the off status. Option-click the icon again will toggle to switch on to allow incoming notifications.
Incoming notifications will automatically resume the next day. To switch off notifications permanently, use the System Preferences>Notification to turn off notifications on per app basis. There is no quick way to switch off notifications for all apps at once.