Here's some tips to would-be FaceTimers:
First, make sure FaceTime is enabled. Tap 'settings' on your new iPhone, scroll down to the green icon called 'Phone' and select it. The second item down is labeled FaceTime. Make sure it is turned on. It may take a moment for FaceTime to become active so make sure you get a confirmation.
Now when you call someone you'll see an on-screen FaceTime icon. You can tap it, and the other person, assuming they are on Wi-Fi and have an iPhone 4, will get an invitation. If he or she accepts you'll be chatting in just a few seconds.