You can redirect the debug output to a text file by adding a TextWriterTraceListener to the Debug.Listeners collection.

public static void Main(string[] args)
{
    TextWriterTraceListener myWriter = new TextWriterTraceListener(@"debug.txt");
    Debug.Listeners.Add(myWriter);
    Debug.WriteLine("Hello");

    myWriter.Flush();
}

You can redirect the debug output to a console application's out stream using a ConsoleTraceListener.

public static void Main(string[] args)
{
    ConsoleTraceListener myWriter = new ConsoleTraceListener();
    Debug.Listeners.Add(myWriter);
    Debug.WriteLine("Hello");
}

Writes to the trace listeners in the Listeners collection when the application is compiled in debug configuration.

public static void Main(string[] args)
{
    Debug.WriteLine("Hello");
}

In Visual Studio or Xamarin Studio this will appear in the Application Output window. This is due to the presence of the default trace listener (opens new window) in the TraceListenerCollection.