One of the common technical support requests we are receiving these days has to do with connecting the MacBook Air to a projector. This has changed just enough from the previous MacBook and OSX operating system to cause confusion. Here are the steps you need to follow.
1. Connect the Lightning to VGA dongle to your MacBook Air
2. Connect the VGA cable from the projector to the dongle (VGA is a 15-pin connector, arranged in three rows of pins. The overall shape of the connector is a trapezoid. Be sure to align the shape properly or you may bend the pins.)
3. On the MacBook, go to System Preferences>Displays. If the cables are connected and everything is functioning properly, you will see three tabs across the middle of the Display window; Display/Arrange/Color. Click on Arrange, and then click the button that says, Mirror Displays.
That should do it! If you wish to read more, you can check out the Apple support document here.