DFU mode is signified by having a completely black screen on the device.
Connect the iPhone to your computer and launch iTunes. Turn the iPhone off (hold down the power button at the top of the iPhone).
Hold down the sleep/power button and home button together for exactly 10 seconds, then release the power button.
Continue to hold down the Home button until a message appears in iTunes telling you an iPhone in recovery mode has been detected by iTunes.
Thanks jermainepaul! I had an iPhone 5 with an expired iOS 7 Beta that would not restore no matter what I tried. I suspect a prior user may have jailbroken it. I must have tried at least 20 times to restore using the latest 7.1 ipsw downloaded from Developer Center. I kept getting Error 3194.
I went into DFU mode following your directions and then the restore worked perfectly the FIRST time! Many thanks!!