The Notification Center can be used in a variety of ways, or not used at all. Its up to you.
The first thing to note is that if you are using LuckNews as the active application, perhaps you are reading news in it, and new Articles arrive the Notification Center will not show those new Article's. This is the default behavior for the Notification Center - the active application does not notify of new content.
One way to use the Notification Center would be to launch LuckNews and then to close its window by clicking in the red circle in the title bar or by selecting the 'Close Window' menu item in the File menu. Now LuckNews is running but not getting in the way of your other windows. When a new Article arrives, you will be notified. You can open the Notification Center and click on a Notification to see the Article in LuckNews.
You can also customize LuckNews to interact with the notifications in different ways. I find I have several very active Subscriptions and other less active but very interesting Subscriptions. I wanted to solve the problem of the less frequent but interesting articles being lost in the noise of the more frequent Subscriptions. The way you can solve this is through the use of Folders.
Each folder allows you to control its notifications in two ways:
The last two check boxes control how a folder handles notification. The first option controls whether or not any unread articles that are contained in a folder are added to the unread count for the application badge in the Dock. So for example, I group my frequently updated Subscriptions into a folder and turn this option off. In that case I know that there will always be more articles to read in that category and I don't need to have the Application Badge show me.
The second option controls whether or not newly arrived Articles in a folder are forwarded to the Notification Center. Turn this off if you don't want to be notified of articles in certain categories.