If you're currently holding a brand-new iPhone 5s in your hot little hands, you know that it'll walk you through adding in your fingerprint when you set it up for the first time. From then on, you can use that fingerprint to unlock the device or to authorize iTunes/iBooks/App Store purchases. OhmyGOSH that rocks.
After you do that, though, you can actually go in and set up additional fingerprints, including those of your friends or family members if you want them to be able to unlock your iPhone, as well. So to configure more of them, go to Settings> General> Passcode & Fingerprint. You'll first have to enter the four-digit passcode you picked when you set up the phone, but then you'll look for a section labeled Fingerprints:
Touch that, and on the subsequent screen, you'll see your current settings for how to use them. To put in a new one, touch Add a fingerprint:
Let your iPhone walk you through the process of scanning an additional finger, or ask your spouse or friend (or, apparently, even your cat) to follow along, and you're finished! Easy as can be, right?
My experience with Touch ID so far has been incredibly positive. Granted, I've owned my 5s for all of three hours, so time will tell, but I haven't had a single issue with unlocking my phone or with test downloads from the App Store. I'm really looking forward to not having to enter my silly Apple ID anymore, let me tell you.