Anymore, your are going to have to configure either an outbound relay or connection that goes to a host that knows how to send mail outbound OR your own smtp, which will require configuring properly for Internet smtp routing. There was a time when you could send outbound from almost any smtp, even one from your own private network, but those days are over (spam would have been worse if still allowed).
If you are running your own "domain" of services, you'll need to configure an smtp for outbound mail. Usually it will just look at the address and figure if it's not handled locally then it will route to the MX record associated with the domain that might handle it.
If you are subscribing to services provided by someone else on behalf of your domain, they should be able to tell you out to reach their server (usually requiring some kind of auth) to send outbound from your network.