Log in.
Click 'User CP'.
Under 'Settings and Options', click 'Edit Options'.
In the Messaging and Notification panel|Private Messaging, tick 'Enable Private Messaging'.
Tick 'Receive Email Notification of New Private Messages'.
Tick 'Show New Private Message Notification Pop-up'.
There are other options available.
Assuming you have notiifed an email to be used, of course. eg exascot at hotmail dot com, for instance. That's also in the CP, 'Edit email and Password'.