In order to use the AirPlay feature of your Mac with an AppleTV, follow the instructions below:
Ensure that the AppleTV is on. Grab the AppleTV Remote and push the menu button and be sure that the status light on the front of the device is on. (see below)
Make sure that the AppleTV is not prompting you for some action. Is should be on the AirPlay screen or the Main Menu screen OR
If you do not see one of the screens above, locate your projector or TV remote and press the source button until the HDMI source is selected
You may be prompted to enter a code on your computer--- this code will be displayed on the projector screen. Enter it into your device.