Are you talking about while running the application in the debugger or a Release version?
If it's the former then, as I said, Console.WriteLine will write to the Output window. It's generally preferable to use Debug.WriteLine because that code can be left in and will simply be ignored by the compiler in a Release build but there can be times where Console.WriteLine is better.
If it's the latter then why not just create your own form with a single-line TextBox for input and a multi-line TextBox for output?
Regardless, I don't think that it's possible to display a console window for the same process in a WinForms app. You could start a new process and communicate with that via its standard input and output streams, but then it's not going to have access to the data in your app.