During normal use, the iPhone does not turn off. When you press the "Sleep/Wake" button or leave your phone alone for a few minutes, the screen shuts off, but the system itself remains active, keeping your apps running, your music playing and your alarms set. To actually turn an iPhone off and back on, you need to hold down "Sleep/Wake" rather than pressing it quickly.
Press and hold the "Sleep/Wake" button on the iPhone for three seconds to display the power off slider. Swipe the slider from left to right to shut down.
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Wait until the backlight on your phone turns off -- you might see a lit black screen for several seconds beforehand -- and then press and hold "Sleep/Wake" again until the Apple logo appears.
Swipe from left to right to unlock your iPhone.
Type in your pass code, if you have one, to reach the home screen. If you have an iPhone 5s or newer and set up Touch ID, you can alternatively place your thumb on the "Home" button to unlock via fingerprint. Even if you set your pass code to activate after several hours of disuse, you need to enter it the first time you unlock the phone after rebooting.