Apple StoreElgato Systems, makers of EyeTV, offers a nice online explanation of how their product works with Apple’s new Apple TV:

EyeTV puts your TV recordings into iTunes: With EyeTV, watch television on your Mac and record TV shows directly to your hard drive. EyeTV has an easy “iPod Button” to export EyeTV recordings into iTunes, where they automatically appear under “TV Shows.” This puts your own content on your iPod, and now, your live TV recordings on Apple TV.

Apple TV puts your iTunes content on TV: When an Apple TV is connected, iTunes automatically detects and synchs with it. That way, your Apple TV box always contains the latest content from iTunes, including the EyeTV recordings you exported there. Apple TV puts that content onto your widescreen TV.

Elgato is working to integrate Apple TV and EyeTV even further and invites Mac users to join their mailing list to be notified of future enhancements.

The company also offers two QuickTime demo videos:
1. How to use EyeTV’s iPod button to add your recordings to iTunes
2. How to send new EyeTV recordings to iTunes automatically

More info and the videos here.