How do I power off my Apple TV?

Go to Settings > Sleep Now

Or, go to the main menu and hold down Play/Pause for five seconds.

It only sleeps, not turns completely off.

Go into Settings, and select "Sleep Now"

Put your Apple TV in sleep mode - Apple Support

As the link suggests, the easy way (for ATV 4) is to hold the Home button until the Sleep popup appears, then select it.

Note that it goes to sleep, not off. It remains connected to the network, and may download updates, screen savers, etc. while sleeping. In this state it may wake up if an AirPlay connection is made to it. If you really need it to be off, the only way is to disconnect it from power, but this is not recommended.