One of the best new features of Apple's iOS 6 that came out last week is the Do Not Disturb function. Admittedly, with enough practice and fiddling, you can get the same result without this option, but the ease of toggling it on, coupled with the available options is welcomed. Here's a quick exploration of some different options you have to keep your phone from disturbing you.
Beyond turning off your phone completely, here are a few options for keeping your phone hushed, but still on for important (or not so important) notifications throughout the day. It could be the difference between being "that guy/girl" and being a polite phone user out in public.
1. Vibrate: I've set my phone to be quiet most of the time, with vibrate and flash as my primary notification system. Since I trained myself to be able to wake up by simply using the vibrating alarm, vibrate doesn't work as well for me. But vibrate mode can be extremely useful when your phone is in hands, but you don't want to impose a ringer on everyone else. Settings > Sounds > Vibrate on Ring.
2. Silent Mode: If you don't want your phone to vibrate at all, then just switch off the sound and ringers from the Settings > Sounds screen. Your phone will be eerily quiet until you reactivate it.
3. Do Not Disturb: This mode silences all of your notifications entirely, and if you use the Reply with Message feature, you can respond to missed calls with an SMS that lets them know why you are unavailable.
Some Android launchers and dialers include this, but it depends on the manufacturer. If you've upgraded to iOS 6, go to Settings - > Do Not Disturb. You can set up a VIP list, allowing your favorites' calls to come through. Also, if you enable the Repeated Calls mode, if someone calls you repeatedly, your phone will ring (helpful for those emergency calls).
4. Airplane Mode: If Do Not Disturb falters and you still receive notifications, or you want to just shut your phone up, but still use some apps, then just switch on airplane mode. When I'm on the go and running out of power, I'll switch this mode on to conserve juice. Just note, you'll be completely cut off from notifications and calls until you turn this off.
5. There's an app for it!: perhaps your problem isn't that you need to keep your phone completely silent, but only specific to a person or unwanted callers. Ringtone Maker Plus Silent Sound lets iPhone users assign silent ringtones to specific numbers/callers, so you'll hear that important call from your better half, but will easily ignore annoying wrong numbers.
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• Slip On Additional Functions with These Sleeves
(Image: Gregory Han)

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2. Silent Mode . . . switch off the sound and ringers from the Settings > Sounds screen...
Or you could just flick the silent button on the side of the phone.
I don't know about the Do Not Disturb option, but I know very well from working in live theater that Airplane Mode DOES NOT disable any alarms you may have set. At least three times a week, some person who has politely turned their phone to Airplane mode gets mortified (and a thousand other people get enraged) when a loud, clear ringtone comes crashing through a silent theater, and gets louder and louder as the phone is hastily jostled out of a pocket or a purse, because there is some previously-set alarm that Airplane mode does not affect. Alarms also are not affected by switching the toggle to vibrate - you'd have to manually go into the alarm settings and change the type of alarm to affect the alarm sound - and even then, you'd be surprised how loud a vibrating phone can sound in a silent theater. Double-check your alarm settings to be sure all potentially disrupting alarms are disabled, or (my preference) just turn your phone off completely.
It's amazing how many people seem to set alarms to go off at precisely the quietest, most meaningful moment in Broadway shows.... ;)
turn it off? the world will still be there in a couple of hours?