I recommend looking over this documentation for the ABNewPersonViewController class.
The setup I would use is to setup an IBAction to your "Add Contact" button. The IBAction can create an instance of the New Person VC.
If you need to predefine some of the fields for the new contact, you will need to create an ABRecordRef and set the properties you want to be in the new contact. Then set the New Person VC's displayedPerson
property to this record.
At the end of the method, you can call `[self.navigationController presentViewController: newPersonVC];
This may be possible in a storyboard, but I have always found it easier to do in code.
Hopefully this will help.