How to connect an iPad to a digital projector
It is actually very simple. 
You just need the right cable.

Depending on Projector type you might use the Lightning to VGA Adapter if your Projector is of that type. Note: it does not support Audio!.
Look at your Projector to see if the plug looks like this:



If your projector has HDMI plug use the Lightning Digital AV Adapter

Look at your projector if the plug looks like this:


The projectors normally have 16:9 = wide screen (for movies) and you iPad does not, so you will see a black stripe on both sides, that is normal.

PS: if it has both plugs pick the second one "Lightning Digital AV Adapter" since you can use it to plug in to your LCD TV :)