There are two ways to close apps in Windows 8 on a touch-screen tablet like the Surface:
1) When the app is displayed in full-screen mode, you can simply tap the top of the app and drag it to the bottom of the screen. The app should automatically close.
2) The second option is by launching your task manager. Do this from the Search icon on the Windows Charms panel. To activate your Charms, swipe right on the right-hand side of your screen. Tap the search icon, and type in
Task Manager. Now, you should see a list of running apps on your tablet. Click the app you’d like to close and hit “End Task.”
NOTE: You can also close apps on laptop and desktop versions of Windows 8 as well. When you’re viewing an app in full-screen mode in Windows 8, hover your mouse over the top of the screen until your cursor turns into a hand. With the hand shown, drag the app to the bottom of the screen to close it: