TestAsync.cs

using System;
using System.Collections.Generic;
using System.Linq;
using MonoTouch.Foundation;
using MonoTouch.UIKit;
using System.Threading.Tasks;

namespace TestAsync
{
  // The UIApplicationDelegate for the application. This class is responsible for launching the 
	// User Interface of the application, as well as listening (and optionally responding) to 
	// application events from iOS.
	[Register ("AppDelegate")]
	public partial class AppDelegate : UIApplicationDelegate
	{
		// class-level declarations
		UIWindow window;
		UIViewController viewController;

		// This is the main entry point of the application.
		static void Main (string[] args)
		{
			// if you want to use a different Application Delegate class from "AppDelegate"
			// you can specify it here.
			UIApplication.Main (args, null, "AppDelegate");
		}

		//
		// This method is invoked when the application has loaded and is ready to run. In this 
		// method you should instantiate the window, load the UI into it and then make the window
		// visible.
		//
		// You have 17 seconds to return from this method, or iOS will terminate your application.
		//
		public override bool FinishedLaunching (UIApplication app, NSDictionary options)
		{
			window = new UIWindow (UIScreen.MainScreen.Bounds);
			
			viewController = new TestController ();
			window.RootViewController = viewController;
			window.MakeKeyAndVisible ();
			
			return true;
		}
	}

	public class TestController : UIViewController
	{
		public override async void ViewDidAppear (bool animated)
		{
			Console.WriteLine ("Starting ViewDidAppear...");

			base.ViewDidAppear (animated);

			await Task.Delay(1000);

			var alert = new UIAlertView();
			alert.Message = "Great work...";
			alert.DismissWithClickedButtonIndex(alert.AddButton ("Ok"), true);
			alert.Show();
		}
	}
}

TestAsync.csproj

<?xml version="1.0" encoding="utf-8"?>
<Project DefaultTargets="Build" ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
  <PropertyGroup>
    <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
    <Platform Condition=" '$(Platform)' == '' ">iPhoneSimulator</Platform>
    <ProductVersion>10.0.0</ProductVersion>
    <SchemaVersion>2.0</SchemaVersion>
    <ProjectGuid>{549E5E7E-1300-415A-B6B8-B93BE19035BA}</ProjectGuid>
    <ProjectTypeGuids>{6BC8ED88-2882-458C-8E55-DFD12B67127B};{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}</ProjectTypeGuids>
    <OutputType>Exe</OutputType>
    <RootNamespace>TestAsync</RootNamespace>
    <IPhoneResourcePrefix>Resources</IPhoneResourcePrefix>
    <AssemblyName>TestAsync</AssemblyName>
  </PropertyGroup>
  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|iPhoneSimulator' ">
    <DebugSymbols>true</DebugSymbols>
    <DebugType>full</DebugType>
    <Optimize>false</Optimize>
    <OutputPath>bin\iPhoneSimulator\Debug</OutputPath>
    <DefineConstants>DEBUG;</DefineConstants>
    <ErrorReport>prompt</ErrorReport>
    <WarningLevel>4</WarningLevel>
    <MtouchLink>None</MtouchLink>
    <ConsolePause>false</ConsolePause>
    <MtouchDebug>true</MtouchDebug>
  </PropertyGroup>
  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|iPhoneSimulator' ">
    <DebugType>full</DebugType>
    <Optimize>true</Optimize>
    <OutputPath>bin\iPhoneSimulator\Release</OutputPath>
    <ErrorReport>prompt</ErrorReport>
    <WarningLevel>4</WarningLevel>
    <MtouchLink>None</MtouchLink>
    <ConsolePause>false</ConsolePause>
  </PropertyGroup>
  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|iPhone' ">
    <DebugSymbols>true</DebugSymbols>
    <DebugType>full</DebugType>
    <Optimize>false</Optimize>
    <OutputPath>bin\iPhone\Debug</OutputPath>
    <DefineConstants>DEBUG;</DefineConstants>
    <ErrorReport>prompt</ErrorReport>
    <WarningLevel>4</WarningLevel>
    <MtouchDebug>true</MtouchDebug>
    <ConsolePause>false</ConsolePause>
    <CodesignKey>iPhone Developer</CodesignKey>
  </PropertyGroup>
  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|iPhone' ">
    <DebugType>full</DebugType>
    <Optimize>true</Optimize>
    <OutputPath>bin\iPhone\Release</OutputPath>
    <ErrorReport>prompt</ErrorReport>
    <WarningLevel>4</WarningLevel>
    <CodesignKey>iPhone Developer</CodesignKey>
    <ConsolePause>false</ConsolePause>
    <MtouchUseLlvm>true</MtouchUseLlvm>
    <MtouchI18n />
    <MtouchArch>ARMv7</MtouchArch>
    <IpaPackageName />
  </PropertyGroup>
  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Ad-Hoc|iPhone' ">
    <DebugType>full</DebugType>
    <Optimize>true</Optimize>
    <OutputPath>bin\iPhone\Ad-Hoc</OutputPath>
    <ErrorReport>prompt</ErrorReport>
    <WarningLevel>4</WarningLevel>
    <CodesignKey>iPhone Distribution</CodesignKey>
    <BuildIpa>true</BuildIpa>
    <ConsolePause>false</ConsolePause>
    <CodesignProvision>Automatic:AdHoc</CodesignProvision>
  </PropertyGroup>
  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'AppStore|iPhone' ">
    <DebugType>full</DebugType>
    <Optimize>true</Optimize>
    <OutputPath>bin\iPhone\AppStore</OutputPath>
    <ErrorReport>prompt</ErrorReport>
    <WarningLevel>4</WarningLevel>
    <CodesignKey>iPhone Distribution</CodesignKey>
    <ConsolePause>false</ConsolePause>
    <CodesignProvision>Automatic:AppStore</CodesignProvision>
  </PropertyGroup>
  <ItemGroup>
    <Reference Include="System" />
    <Reference Include="System.Xml" />
    <Reference Include="System.Core" />
    <Reference Include="monotouch" />
  </ItemGroup>
  <ItemGroup>
    <Folder Include="Resources\" />
  </ItemGroup>
  <ItemGroup>
    <None Include="Info.plist" />
  </ItemGroup>
  <ItemGroup>
    <Compile Include="AppDelegate.cs" />
  </ItemGroup>
  <Import Project="$(MSBuildBinPath)\Microsoft.CSharp.targets" />
</Project>