To set it up, first you have to update to iOS 9.3. Then go to Settings > Display and Brightness > Night Shift and select what time you want it to turn on. You can create a custom schedule, or set it to run from sunset to sunrise -- which it automatically detects based on whatever time zone you're in. And if you suddenly find yourself in some romantic mood lighting and want to enable it on demand, there's an easy shortcut via the Control Center: swipe up from the bottom of the screen and tap the sun/moon icon.
You may notice that Night Shift doesn't work while you're in Low Power Mode -- and that's by design, since it does eat up a decent amount of battery energy. However, the smartypants at 9to5Mac discovered a neato workaround that involves asking Siri to help you out so you can use both features at once.