Turns out there's a manual! You should probably get it...
Most people know you can "really" shut down the iPhone by pressing and holding the Sleep/Wake Button until the red slider appears.
To restart the iPhone, click and hold the Sleep/Wake button until the Apple logo appears.
You can take a screen shot by clicking the Sleep/Wake button while holding down the Home button. The picture will be added to your built-in Photo library and can be managed just like pictures you take with the camera.
You can access the iPod controls without unlocking ("slide to unlock") by double-clicking the Home button. You can also do this while running other applications. Here, I've brought up the iPod controls while browsing in Safari.
Here's an example showing the iPod controls while music was playing. The iPhone was locked, but double-clicking the Home button brought up the controls and showed the currently playing selection.
You can change this behavior if you want to use double-clicking the Home button for something else. Go to Settings:General:Home Button to change it. Changing this setting only changes the behavior when you're running applications. Double-clicking when the phone is locked will still bring up the iPod controls.
If you click (well, squeeze actually) the Mic button while the iPhone is locked, it will resume playback of the current iPod selection.
Double-clicking will jump to the next selection.
Triple-clicking will go back to start of this selection. If you're already at the start of a track, triple-clicking will go to the previous track.
Like most cell phones, you can silence an incoming call by pressing one of the volume buttons.
To decline a call and send it straight to voice mail, click and hold the Mic button for a couple seconds then let go. You'll hear two beeps letting you know the call was declined.
If you're not using the headset, you can decline a call by double-clicking the Sleep/Wake button on the top of the phone.
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