From http://developer.xamarin.com/guides/ios/user_interface/introduction_to_storyboards/

launch_storyboard_view

public partial class AppDelegate : UIApplicationDelegate
    {
        UIWindow window;
        public static UIStoryboard Storyboard = UIStoryboard.FromName ("MainStoryboard", null);
        public static UIViewController initialViewController;

        public override bool FinishedLaunching (UIApplication app, NSDictionary options)
        {
            window = new UIWindow (UIScreen.MainScreen.Bounds);

            initialViewController = Storyboard.InstantiateInitialViewController () as UIViewController;

            window.RootViewController = initialViewController;
            window.MakeKeyAndVisible ();
            return true;
        }

    }