I get the impression I'm supposed to define a class or something for this form (or maybe this works as intended in VS2010?) but the lesson does not say how.
You're on the right track! In this project you need to add a couple of forms for the code to display as dialogs.
Open the Project menu and select Add Windows Form. Then use the Properties window to change the form's name to "GettingThereForm" and you should be all set.