how do I airplay from my Mac to Apple TV?

AirPlay video and mirror your device's screen

AirPlay to Apple TV on iPhone, iPad, and Mac

System Preferences->Displays. At the bottom of the Displays preference panel you will see the AirPlay display options. Assuming your Mac and your Apple TV are on the same WiFi network you should see your Apple TV on that option list. At the very bottom is a box to check that will give you access to the Displays options in your top screen menu. You can then select your Apple TV from the top menu anytime you want.