To use an external SMTP server, follow this manual:

====== 1.) Edit main.cf ======
Open /etc/postfix/main.cf and add this lines:

<cli>
relayhost = smtp.domain.tld
smtp_sasl_auth_enable = yes
smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd
smtp_sasl_security_options = noanonymous
smtp_sasl_mechanism_filter = plain, login
</cli>

====== 2.) Edit sasl_passwd ======
Open /etc/postfix/sasl_passwd and add this:

<cli>
smtp.domain.tld username:password
</cli>

====== 3.) Run postmap command and restart postfix ======
Run this line:

<cli>
# postmap hash:/etc/postfix/sasl_passwd
</cli>

===== Now, restart postfix =====
<cli>
# /etc/init.d/postfix restart
</cli>

Important: SMTP server like smtp.googlemail.com don't work!