how do I get my iPhone to print with AirPort?

iOS: AirPrint 101

Having AirPort Utility installed unfortunately will not help.

You need to have an AirPrint compatible printer if you want to be able to print directly from the iPhone.

Check this Apple support document to see if your printer might be compatible.

http://support.apple.com/kb/HT4356

If your printer is not compatible, an App like Print Central installed on the iPhone might allow you to print from the iPhone.

App Store - PrintCentral for iPhone/iPod Touch

Check with Print Central support to see if your model might work with the App.