I read the docs at the Zimbra Wiki
and followed these steps:

zmprov ms mail.internal.com zimbraMtaRelayHost smtpout.secureserver.net:80
echo smtpout.secureserver.net john@example.com:password > /opt/zimbra/conf/relay_password
postmap hash:/opt/zimbra/conf/relay_password
postmap -q smtpout.secureserver.net /opt/zimbra/conf/relay_password
postconf -e smtp_sasl_password_maps=hash:/opt/zimbra/conf/relay_password
postconf -e smtp_sasl_auth_enable=yes
postconf -e smtp_cname_overrides_servername=no
postfix reload
postconf -e smtp_use_tls=yes
postfix reload
john@example.com is the external godaddy account which I plan to use for relaying.

I still cannot send emails to external accounts:

The error message I see is:

Jun  1 04:22:58 mail postfix/qmgr[7867]: 2C2F35838008: to=, relay=none, delay=212705, delays=212705/0.03/0/0, dsn=4.4.3, status=deferred
(delivery temporarily suspended: Host or domain name not found. Name service error for name=smtpout.secureserver.net type=MX: Host not found, try again)
Also, for another ID

Jun  1 07:18:49 mail postfix/qmgr[7867]: D4AB05838002: to=, relay=none, delay=231400, delays=231348/51/0/0, dsn=4.3.0, status=defer
red (mail transport unavailable)
Any help will be greatly appreciated.