Do you mean how can you tell if the relay accepted the email? If so, have a look in /var/log/maillog for something like this:
Feb 9 05:14:33 myhostname sm-mta: n18JEVEK030540: to=<email@example.com>, ctladdr=<firstname.lastname@example.org> (1016/132), delay=00:00:01, xdelay=00:00:01, mailer=relay, pri=120437, relay=smart.host.address.au. [203.x.x.x], dsn=2.0.0, stat=Sent (ok: Message 451228879 accepted)
The status of stat=Sent (ok: Message 451228879 accepted)
tells you that the smart host has received the email from your SMTP server.
Do you mean how do you tell that the email has been delivered to the final recipient? If so, you either need to request a receipt notification with your email client (not reliable) or get access to the smart host's logs. I'm told you can also request the DSN information but I haven't had to do that myself.