iOS 6

Press the home button to get to the iOS home screen.

Tap the home button twice, quickly. This will bring up a tray of icons with the open apps at the bottom.

Press and hold an app icon in the bottom drawer until they begin to shake with an (-) on the corner of it.

Tap the the app icon you want to close. It will disappear and the apps will slide over. The app is now closed.

Click the Home button again and the bottom tray will disappear.

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iOS 7

Press the home button to get to the iOS home screen.

Tap the home button twice, quickly. This will reveal all apps that are open. Swipe left or right to locate the app to close.

 

Swipe the app up off the screen. The app is now closed.