class Program
{
    static void DoIt(string entry)
    {
        Console.WriteLine("Message: " + entry);
    }

    static async void DoIt2(string entry)
    {
        await Task.Yield();
        Console.WriteLine("Message2: " + entry);
    }

    static void Main(string[] args)
    {
        // old way
        Action<string> async = DoIt;
        async.BeginInvoke("Test", ar => { async.EndInvoke(ar); ar.AsyncWaitHandle.Close(); }, null);
        Console.WriteLine("old-way main thread invoker finished");
        // new way
        DoIt2("Test2");
        Console.WriteLine("new-way main thread invoker finished");
        Console.ReadLine();
    }
}

Task.Run(A);

static async void FireAndForget(this Task task)
{
   try
   {
        await task;
   }
   catch (Exception e)
   {
       // log errors
   }
}

MyTaskAsyncMethod().FireAndForget();

Task.Factory.StartNew(() => DoIt2("Test2"))

public async void Method()
    {
        //Do UI stuff
        await SomeTaskAsync();
        //Do more UI stuff (as if called via Invoke from a thread)
        var nextTask = NextTaskAsync();
        //Do UI stuff while task is running (as if called via BeginInvoke from a thread)
        await nextTask;
    }