The idea is to call an action that opens the UIPicker when the user taps the UITextField. Because the UITextField does not responde to the usual touchUpInside events that UIButtons respond to, I would just overlay a transparent UIButton on top of the UITextField and just in case, make the text field's userInteractionEnabled property NO. Hook the UIButton to responde to touchUpInside and call a method that opens the UIPicker. Another option would be an immediate response to the text field's touch by implementing "textFieldShouldBeginEditing" and immediately resigning the text field.
The next step would be to present the UIPicker - if we are talking about iPad, this would best be done by using a UIPopoverController. On iPhone, maybe consider bringing it up modally. When you create the view controller that holds this UIPicker, be sure to add a delegate property to it so that whatever value that was selected on the picker can be transfered back to the main view controller and on to the UITextField.
Hope this helps with getting you started.