When you have notifications, they will appear in a red 'bubble' on the notification button:
When you click this button you will see a simple view of your most recent notifications. You can click into them from here individually, or click 'View all notifications' to see a complete list.
From the page of all pending notifications, you can click the plus icon next to any notification to see the details which will open up in a side panel. From here, you can also clear the individual notification by clicking 'Complete' from the bottom right of the side panel.
You can clear multiple notifications simultaneously using the buttons in the top right of the list by either selecting specific notifications and clicking 'Mark selected notifications as complete'. You can clear all of them using the 'Mark all notifications as complete'.