I have had a few teachers ask recently how to project their ipods and ipads. There are a few ways to do it, including purchasing a projector specially designed for your iDevice, but assuming you already have a general purpose projector, here are 2 ways to “get'er done”.
You can use a 3rd party application called AirServer (http://www.airserver.com/) which enables you to use Airplay on your computer. This is the best way to wirelessly project the ipad (works only with iPad 2 and above). You can also use Airplay to project newer ipod touches and ipods (4S and above for iPhones, and 5 and above for iPods) If the computer is connected to a projector then you can see it on the Projector. The computer and the iDevice need to be on the same wireless network in order to work.
To project without a computer you can only do it wired with an adapter and the cord that comes with the iPAd. This will mirror the newer ipods, and IPad 2 and above, but will only play videos or images (not mirroring of the full screen) for older iPod touches (ipod 4 and below or ipad 1). You can purchase a VGA adapter or a HDMI adapter from the apple store.
For newer devices with Lightning port: http://store.apple.com/ca/product/MD826ZM/A/lightning-digital-av-adapter?fnode=3a
For older devices with 30 pin port: http://store.apple.com/ca/product/MD098ZM/A/apple-digital-av-adapter?fnode=3a
For newer devices with Lightning port: http://store.apple.com/ca/product/MD825ZM/A/lightning-to-vga-adapter?fnode=3a
For older devices with 30 pin port: http://store.apple.com/ca/product/MC552ZM/B/apple-vga-adapter?fnode=3a