When you buy the Apple TV device you only pay the one time fee for the Apple TV device to stream content over your WiFi internet.
So there's no fee to actually use your Apple TV device once you buy it and Apple does not charge you a monthly fee for use of the Apple TV device.
But if you want to watch certain shows and content then you'll need to pay a monthly fee for those channels and content on the Apple TV device.
Most people do pay between $30.00 per month to $45.00 per month to use their Apple TV device depending on the channels they want and the content they want to stream through their Apple TV device.