I recently stumbled across a blog post that talked about how to project your iPad to a projector on the TeachingWithiPads.com site. I liked both methods described in the article, but I was able to quickly implement Method 2, in 10 minutes.
Method 1: Use AirPlay with AppleTV to projector (or in some cases a TV monitor.)
Method 2: Use Reflector software, installed on a Mac (or PC) that is hooked up to the projector.
I purchased the Reflector software for $12.99 and was able to install it on my MacBook via download and activation. I turned on my iPad and made sure both devices were on the same WiFi network. I double clicked the “home” button and swiped right to get the AirPlay activation.
I selected “my computer” and turned on “Mirroring” and viola I was up and running.
Reflection in Full Screen
Reflection on the Desktop