Apple provides a nice framework for incorporating Address Book access into your iOS application, using the familiar UI from the Contacts app. They provide some nice documentation on this UI in the section User Interaction: Prompting for and Displaying Data.
Here is an example of the UI that Apple indicates is available:
The default UI is a little different
The above view of the controllers looks great, but getting them to work together as the images imply is not quite so straightforward. Consider the following code snippet used to present the People Picker: