Here is a link to a webpage that gives you a detailed explanation with pictures. Although it describes how to hook up the ipod to a TV, it is exactly the same for a projector. More than likely from your description you already have the wires, so you need to enable the video settings.
Setting up your iPod video options lets you control how you export
video. The iPod Video Options screen selects how your iPod handles
video file playback.
To open these settings, choose Videos -> Video Settings from your
main iPod menu. This screen offers three settings: TV Out, TV Signal
and Widescreen. Adjust to produce the video playback style you need.
Use this setting to choose from:
- No. Playback remains on the iPod itself.
- Yes. A TV signal is produced.
- Ask. The iPod prompts you whenever you play a video file.
I hope this helps and good luck. Please vote and leave a comment.