This tutorial explains to how to enable the Sleep mode of your Apple TV. If it is your first time using an Apple TV, then you will be surprised to see that there's no On/Off button on the device. The only alternatives available to power off the device is either to unplug it or enable the Sleep mode. By default the Apple TV will go to sleep (standby) mode after a certain period of activity, but nonetheless you can activate this setting manually:

You can put your Apple TV to sleep by going to the Settings menu and then select Sleep Now. Then again the same result can be achieved by pressing the Play/Pause button of the Apple TV remote for a couple of seconds while you are in the main menu (press the Menu button on your remote).

You can also configure the auto-sleep settings your Apple TV by going to Settings > General > Sleep After and select after how much time (15 minutes, 30 minutes,...) the device will go to sleep.

Press the Menu button to exit from standby mode.