How do you get the camera to recognize and respond to QR codes?

For the camera app, check to see that Settings > Camera Scan QR codes is turned on

You can also use the QR code scanner in Control Center.. that one may be more convenient for some because it will automatically launch the website rather than requiring you to tap on the screen. It also has a flashlight option in case the barcode needs better lighting.

If neither method works, the code you are trying to scan may not be a QR code

Scan a QR code with the iPhone camera – Apple Support

If you want to check what kind of barcode it is, you can search the App Store for Cognex Barcode Scanner and one of the top results should be a yellow box with a barcode in the icon and a C in the upper right.. That app is really nice, it's free and it will read & identify the barcode type for you... as well as allow you to navigate in to a website from it

Refer to Apple's set of instructions in Scan a QR code with your iPhone, iPad, or iPod touch - Apple Support:

How to scan a QR code with the Camera app 

1. Open the Camera app from the Home Screen, Control Center, or Lock Screen.
2. Select the rear facing camera. Hold your device so that the QR code appears in the viewfinder in the Camera app. Your device recognizes the QR code and shows a notification.
3. Tap the notification to open the link associated with the QR code.