There are 3 basic ways to close an app in windows 8:
1. In a Metro app you use your mouse and click from the top of the page and drag all the way to the bottom of the screen.
2. ALT + F4 : However I have had mixed or non working with Metro apps
3. Use ALT+CTRL+DEL and kill the application in task manager
If you have a touch screen your option is similar to 1. However you touch and drag to the bottom.
I hope someone finds these useful.
Here is video showing the drag action to close the app.