Got my first iPhone 5 several weeks ago (switched from Blackberry). It took me a little bit to figure out how to turn the ringer off completely so it’s in vibrant mode only. Most of the articles during my search on Google only talked about putting the ringer volume all the way down in the Settings (yet it doesn’t turn the sound off completely) unless you turn on the airplane mode or shut off your phone completely so it’s useless.
So upon further searching I found out that there is a switch on the side of the phone just above the volume buttons is what does the trick. Simply flip the switch so you see the red bar on the switch, everything becomes silent (vibrant is still on)! Simple and easy yet everyone else online is making it complicated.
Note that this trick helps with my purpose but you may want the settings differently such as no vibrate, etc. This is no new trick, my wife’s iPhone 4 has the same switch.