I come from a Windows and physical keyboard world, so things that are simple in Windows seem very complicated or undoable in iOS. For example, shutting down an App (as simple as clicking the red X in the upper right corner of a window) didn’t seem possible in iOS.

Find below some shortcuts that show how to do the “impossible”:

• Go to Standby: Press the Standby button shortly.
• Wake up from Standby: Press the Standby button shortly.
• Go to Home screen: Press the Home button shortly.
• Shutdown the device (Power off): Press the Standby button for several seconds until “Slide to power off” appears. Then slide to the right and the device will power off.
• Switch on the device: Press the Standby button shortly.
• Reboot the device: Press the Standby and the Home button simultaneously for several seconds until the screen goes black and the Apple logo appears.

• Go to a different App, but leave the current App open: Press the Home button and choose a different app from the Home screen.
• Close an App completely: Double-click the Home button: All the open apps will appear. Choose app and swipe it up: The app will close completely (will be removed from memory).
• Delete an App: Tap on an App icon for several seconds. The App icons will start to shake. Tap on the small X on the upper left corner of the app icon to delete it.
• Take a screenshot: Press and hold the standby button and press the home button shortly. The screen will go white shortly and you will hear a shutter. Release the standby button. The screen shot can be found in the camera app under the camera roll.

Update (July 2018): The shortcuts above are correct for the iPhone 6 and below. For newer iPhones, for example for the iPhone X (that does not come with a home button), the key combinations have changed.