Adding a simple UIAlertView

Other answers already provide information for iOS 7 and older, however UIAlertView is deprecated in iOS 8.

In iOS 8+ you should use UIAlertController. It is a replacement for both UIAlertView and UIActionSheet. Documentation: UIAlertController Class Reference. And a nice article on NSHipster.

To create a simple Alert View you can do the following:

UIAlertController *alertController = [UIAlertController alertControllerWithTitle:@"Title"
                                                                         message:@"Message"
                                                                  preferredStyle:UIAlertControllerStyleAlert];
//We add buttons to the alert controller by creating UIAlertActions:
UIAlertAction *actionOk = [UIAlertAction actionWithTitle:@"Ok"
                                                   style:UIAlertActionStyleDefault
                                                 handler:nil]; //You can use a block here to handle a press on this button
[alertController addAction:actionOk];
[self presentViewController:alertController animated:YES completion:nil];

Swift 3 / 4 / 5:

let alertController = UIAlertController(title: "Title", message: "Message", preferredStyle: .alert)
//We add buttons to the alert controller by creating UIAlertActions:
let actionOk = UIAlertAction(title: "OK",
    style: .default,
    handler: nil) //You can use a block here to handle a press on this button

alertController.addAction(actionOk)

self.present(alertController, animated: true, completion: nil)

Note, that, since it was added in iOS 8, this code won't work on iOS 7 and older. So, sadly, for now we have to use version checks like so:

NSString *alertTitle = @"Title";
NSString *alertMessage = @"Message";
NSString *alertOkButtonText = @"Ok";

if (@available(iOS 8, *)) {
    UIAlertView *alertView = [[UIAlertView alloc] initWithTitle:alertTitle
                                                        message:alertMessage
                                                       delegate:nil
                                              cancelButtonTitle:nil
                                              otherButtonTitles:alertOkButtonText, nil];
    [alertView show];
}
else {
    UIAlertController *alertController = [UIAlertController alertControllerWithTitle:alertTitle
                                                                             message:alertMessage
                                                                      preferredStyle:UIAlertControllerStyleAlert];
    //We add buttons to the alert controller by creating UIAlertActions:
    UIAlertAction *actionOk = [UIAlertAction actionWithTitle:alertOkButtonText
                                                       style:UIAlertActionStyleDefault
                                                     handler:nil]; //You can use a block here to handle a press on this button
    [alertController addAction:actionOk];
    [self presentViewController:alertController animated:YES completion:nil];
}

Swift 3 / 4 / 5:

let alertTitle = "Title"
let alertMessage = "Message"
let alertOkButtonText = "Ok"

if #available(iOS 8, *) {
    let alertController = UIAlertController(title: alertTitle, message: alertMessage, preferredStyle: .alert)
    //We add buttons to the alert controller by creating UIAlertActions:
    let actionOk = UIAlertAction(title: alertOkButtonText,
        style: .default,
        handler: nil) //You can use a block here to handle a press on this button

    alertController.addAction(actionOk)
    self.present(alertController, animated: true, completion: nil)
}
else {
    let alertView = UIAlertView(title: alertTitle, message: alertMessage, delegate: nil, cancelButtonTitle: nil, otherButtonTitles: alertOkButtonText)
    alertView.show()
}

UPD: updated for Swift 5. Replaced outdated class presence check with availability check in Obj-C.

UIAlertView is deprecated on iOS 8. Therefore, to create an alert on iOS 8 and above, it is recommended to use UIAlertController:

UIAlertController *alert = [UIAlertController alertControllerWithTitle:@"Title" message:@"Alert Message" preferredStyle:UIAlertControllerStyleAlert];
UIAlertAction *defaultAction = [UIAlertAction actionWithTitle:@"Ok" style:UIAlertActionStyleDefault handler:^(UIAlertAction *action){

    // Enter code here
}];
[alert addAction:defaultAction];

// Present action where needed
[self presentViewController:alert animated:YES completion:nil];

This is how I have implemented it.

When you want the alert to show, do this:

    UIAlertView *alert = [[UIAlertView alloc] initWithTitle:@"ROFL" 
                                                    message:@"Dee dee doo doo." 
                                                    delegate:self 
                                                    cancelButtonTitle:@"OK" 
                                                    otherButtonTitles:nil];
[alert show];

    // If you're not using ARC, you will need to release the alert view.
    // [alert release];

If you want to do something when the button is clicked, implement this delegate method:

- (void)alertView:(UIAlertView *)alertView didDismissWithButtonIndex:(NSInteger)buttonIndex {
    // the user clicked OK
    if (buttonIndex == 0) {
        // do something here...
    }
}

And make sure your delegate conforms to UIAlertViewDelegate protocol:

@interface YourViewController : UIViewController <UIAlertViewDelegate>