First off, make sure that your Apple TV (or other AirPlay capable device) is on the same Wi-Fi (or wired) network as your Mac. This is very important.

Look at your top menu bar, near the clock, for an icon that looks like two horizontal toggle switches. To see what this looks like, look at Apple's page here.

1. Click the Screen Mirroring icon (which looks like two screens, staggered one on top of the other) 2. Choose your Apple TV (or other device) from the options. 3. Once AirPlay has started, you should see an icon in the top bar like a TV with a triangle underneath it. You can click that icon to change between mirroring your Mac screen, or extending to the AirPlay screen (like a second monitor).

1. Click the Apple icon in the upper, left of your screen 2. Click on System Preferences 3. Click on Displays 4. Near the bottom of the window, you should see AirPlay Display. 5. Click on that drop down, and select the device from the list. 6. Once AirPlay has started, you should see an icon in the top bar like a TV with a triangle underneath it. You can click that icon to change between mirroring your Mac screen, or extending to the AirPlay screen (like a second monitor).

Check out Apple's instruction page HERE.

Hope this helped!