The Notifications (previously referred to as Action Center) panel can be accessed either by clicking the icon near the clock (as circled in red below) or if using a device with a touchscreen (e.g. tablet/laptop) by swiping in from the right of the screen

The panel will then appear down the right hand side of your screen (as shown below)

It is divided into two sections:-
Quick Actions - These are the buttons which appear at the bottom of the Action Center window and give you quick access to settings such as tablet mode, airplane mode (turns off all wireless connections for use on planes and other restricted areas), quiet hours (to turn off all audible notifications), creating a Note using OneNote and All settings (which opens up the main settings screen)
Click Edit you quick actions to make changes
By default the most used icons are shown, you can click the Expand button to show them all
Notifications - These appear at the top of the Action Center window, and can be notifications warning about problems, information on new updates, email notifications, calendar reminders etc - you can click Clear all notifications at the bottom to clear all notifications or you can clear them individually by clicking the X next to each item
Both of these areas can be customized by clicking Start > Settings > System > Notifications & actions (as shown below)

You can turn on/off notifications for specific apps by switching the toggle button as shown below, or you can change how an app shows notifications by clicking on the app you wish to change

You can change how the notification is displayed e.g. as a banner or in the Action Centre, choose whether you want a sound to be played and also set the priority of the notification
As per below image you get a notifications visualizer so you can easily see how particular settings will look
