How can I set things up so that, after I or my opponent move, an email notification is sent to us.

@PB1946
click your avatar image at the top right of the page.
click 'settings' in the window that will open.
click 'notification settings' and select your preferences.
make sure to click 'update' at the bottom of that page when done.

<edit> Your opponent will need to adjust their own settings.