The first way involves the Apple Mini DVI to VGA Adaptor. This method requires you to simply plug the adapter directly into the projector and your iPad. Another method is to use mirroring, a feature available on iOS 5.0 and higher.
The Reflector App is also available for $12.99 or $54.99 for multiple licenses, that also allows you to connect your iPad to a computer/projector.
This step-by-step guide explains the steps to mirror your iPad through your projector via mirroring. Please make sure you are referring to the correct projector type. If your projector type isn't listed (I've just posted directions for a couple types that I am used to using) feel free to contact me and I'll do my best to help you out.
Epson Brightlink

- Turn on the projector
- Turn on the Apple iTV (hit the menu button)
- Change the projector setting to Computer 2
- Connect your iPad to the same network that the iTV is connected to.
- Use 4 fingers to swipe up
- Slide all the way to the left and click on the mirroring icon
- Select your Apple iTV
- Slide mirroring to on
Dell Projector
- Turn on the projector
- Turn on the Apple iTV (hit the menu button)
- Change the projector connection to HDMI
- Connect your iPad to the same network that the iTV is connected to.
- Use 4 fingers to swipe up
- Slide all the way to the left and click on the mirroring icon
- Select your Apple iTV
- Slide mirroring to on
Troubleshooting
- Is your iPad connected to the same projector as your Apple TV?
- Is there a password on your Apple TV? Did you enter it
- Is your Apple TV on? (hit the menu button)
- Is AirPlay turned "on" on the Apple TV?
- Still having trouble?