Detailed screen shots are available in the gallery below for each step!
Upgrade to iOS 4 or later. As far as I am aware, this will not work on any older versions of the iPhone operating system. If you still need to upgrade just do it normally through iTunes.
Go to "Settings."
Select "Mail, Contacts, Calendars."
You will see a list of all of your mail accounts. Only the Google ones are important here. Choose the Google account you wish to integrate with the Calendar app. If you have multiple calendars you would like to integrate from different Google accounts, you should be able to simply do these next few steps for each one. If you DON'T see any Google accounts, that is because you haven't set up your gMail account on your iPhone. Just click "Add Account" at the bottom of the page to do so.
You will see a page for your Google account. Toggle on "Calendars" and you are essentially done!
To view your functioning calendar, go back to the Home screen and select "Calendar" (it should have today's date on the icon).
If you see little dots on different days, that means those days have events associated with them. Click around to see if pre-existing gCal events have been integrated.
Congratulations, you're all done!