OK my contract with AT&T was for 2 years and expires on May 7th 2013. I have had my phone since early May of 2011.
Then you have an iPhone 4 and not a 4S, since the 4S didn't come out until October. The iPhone 4 came with iOS 4 (which supported FaceTime, but no icon for it on the iPhone).
You can enable FaceTime in multiple ways, depending on your device: