When Apple launched "Hey Siri" with iOS 8, you could wake your iOS device with the simple command as long as your iOS device was connected to power.
The feature, as useful as it is, had a big problem: It wasn't loyal to only your voice; anyone within earshot could give the command and interact with your device.
With the release of iOS 9, however, Apple has added the ability to teach Siri your voice so (in theory) your iOS device will only listen for you.
I wasn't prompted to go through the setup process when I updated to iOS 9, but I was able to trigger the setup process by going back going to Settings > General > Siri and turning the feature off, then back on.
As soon as you enable it, the setup process begins. You'll be asked to repeat "Hey, Siri" three times, followed by two more commands. Try and go through the process in a somewhat quiet place in order to speed up the process. I originally attempted setup as I was riding in a car and had to repeat the commands numerous times. Once I got home, setup went without an issue.
The process used here is likely the same process iPhone 6S and 6S Plus users will follow as they set up the new iPhone's always-on voice command feature.