Do Not Disturb is a great feature announced at WWDC 2012 with iOS 6. After Control Center made its debut in iOS 7 it got even more convenient to temporarily silence your notifications. A lesser-known feature of Do Not Disturb is that it can be regularly scheduled so your iPhone automatically switches to silent running during certain times of day. I have mine set up to leave me alone "overnight," which I define as between midnight and 6am.
There are a couple of caveats: If you use designate a group of Contacts (and one of those options is the Favorites list in the Phone app), calls from those contacts will come in normally. You can also set up the "repeat" features, which means if the same person calls twice within three minutes, that second call will also come through. Here's how to configure everything:
First, go to Settings > Do Not Disturb:
Here's the Dungeons and Dragons-I mean, Do Not Disturb preferences.
Once there, you can manually activate DND if you like. I'd suggest using this to see the "moon" show up in the menu bar so you can tell the difference between on and off if you aren't a big DND user now. If you look down the screen a little, you'll see the scheduling feature. Turning on the switch will show you what's currently selected; if you haven't set this up previously you'll see the "Quiet Hours" option:
Here you can adjust the start and stop times for Do Not Disturb.
Once that's set up how you like, you can configure the "Allow Calls" feature and the "Repeated Calls" feature (you know, or not, I'm not the boss of you). At the very bottom is the option for whether or not your phone is fully silent during the scheduled time or only while it's locked.
Here's the bottom of the DND screen, where you can roll for initiative. Wait.
This doesn't have to be set for nighttime, you can use it for work hours or afternoon nap time or whatever other time you'd prefer your iPhone to be quiet.