At the top right corner of the site you should see your profile icon. When you have a new notification you will see a number there. If you hover over it a drop down box will appear and let you know what new activity you have on either your questions, answers, messages, etc.
You'll always see that little space at the top right, showing your username, avatar, and Xper level. If you see a number there next to the avatar, it's a notification. Hovering over that area shows the menu, and will tell you exactly where that notification is coming from :-)