You will need to turn on New Ticket Alerts in admin panel > settings. On the same screen,s et your outgoing email address, to eother one you've configured, or set the system to sue php's built-in mail function.
If you are not using the built-in mail() function, you'll need to enter your SMTP server details for the outgoing email address you are using under Emails.
But yes, as PRedmond mentioned, the big question is are you/your staff receiving emails from osTicket?