To sync your Google calendar directly without connecting you’ll need to follow the steps in these two links.
1) Follow the directions here to setup your Google account to sync with your iPhone:
http://www.google.com/support/mobile/bin/answer.py?answer=138740&topic=14252
2) Follow the directions here to choose to sync the Duet calendar on Google to your phone:
http://www.google.com/support/mobile/bin/answer.py?answer=139206