Q:

What is the difference between addChildViewController and presentModelViewController

I know there are three ways to change the view in iOS
1. 
[self addChildViewController:thirdViewController]; 
[contentView addSubview:thirdViewController.view]; 

2. 
First * sVC = [[First alloc] initWithNibName:@"First" bundle:[NSBundle mainBundle]]; 
[self presentModalViewController:sVC animated:YES];

3. 
MyViewController *sampleViewController = [[[MyViewController alloc]initWithXXX] autorelease];       
[self.navigationController pushViewController: sampleViewController animated:true];

pushViewController requires the navigation controller, which I understand.  However, when to use addChildViewController and presentModalViewController?? 

A:

These are four totally different implementations

addChildViewController is used in iOS5 to do viewController containment, this will enable you to easily create your own NavigationCotrollers or TabControllers its only available in iOS5
addSubview is the lowest level of the three, this will just add a view to another view, as a child
presentModalViewController is used to present a viewController modally on the screen, hence overwriting the old one
pushViewController used in UINavigationController to push a new ViewController to the viewcontrollers stack,

A:

1) was introduced in iOS 5 as part of Apple's paradigm shift to allow view controller hierarchies, it just puts a view controller in front of the current one.   You have to manage the flow of controllers. 
2) Is the same as one, except it can only be done for one view controller at a time.   Actually, this method has been superseded by [self presentViewController:animated:completion:]
3) Adds the view controller to a list so you can go back to the previous one after hitting 'back'.   iOS will manage the flow of controllers for you.