Downgrading from iOS 7 to a recent full backup of iOS 6.1.3
Note: this will only work if downgrading from a prerelease beta OS to a regular version.

You can only ever restore an iOS device to the latest public version.

Downgrading is super easy: Just put your iPhone into DFU mode (plug into iTunes, power off, hold down Sleep/Wake and Home button for 8 seconds, let go of the power button and continue to hold down the home button until iTunes alerts you. The screen should be black) and follow iTunes through there.