How do you start a new game in Pokemon Heart Gold?

Answer 1

The previous answer was in fact incorrect... You cannot start a new game simply by going into the new game option. In order to prevent accidentally deleting a previous save file they made it more difficult to do.

What you must do is go onto the screen where you see ho-oh flying around hold down the up button, select and B simultaneously which will allow you to delete your previous file and you can then start a new one.