What is your model Apple TV? Identify your Apple TV model - Apple Support
Set up the Apple TV Remote on your iPhone, iPad, or iPod touch - Apple Support
The Apple TV (4th generation or later) should be straight-forward to pair with, as described, if both devices are already on the same home network. Else you will need an additional functional remote to help set it up.
The Apple TV (3rd generation) needs a functional remote to set up the Apple TV Remote widget in Control Center.
For the Apple TV (3rd generation), your options are:
The Apple TV (2nd generation) is not compatible with the Apple TV Remote widget in Control Center.
For the Apple TV (2nd generation), your option is: