It depends on where you keep your dialog pointer. For example, you can create some signal on your main window and connect it with dialog show() slot(or exec() if you need it to be modal). Or if you keep your dialog pointer in the main windows then you can just use it with show/exec method directly.
As to About->Author menu: for that you should create QAction and add it to the menu. And QAction has triggered() signal which you can connect to exec/show slot of the dialog.