You need to know which SMTP server you have available! I can't know :-) As I understood from your message, it's impossible that you manage a server by yourself inside your internal network, so you need to use an external SMTP server like Gmail or other email providers.
I repeat, it's the same thing of configuring an e-mail client like Outlook. You use SMTP for sending emails, so you have to know which service you bought or that you use for free (like Gmail, f.e.).
I suppose your company for which you are installing osTicket had e-mail mailboxes, so you have an e-mail provider...