Email trough extern SMTP smart relay
If you use a normal Mail Server as SmartHost, it is very simple.
Add or modify in your main.cf the relayhost line, like gertjan describe. On the most systems it is recommended to connect with a user and SSL. For that you will need to add following lines to your main.cf.
Now you need to create a password file where you identify the user with password witch will connect to the smtp server of your provider/mail server.
smtp_sasl_auth_enable = yes
smtp_sasl_security_options = noanonymous
smtp_sasl_password_maps = hash:/etc/postfix/sasl_password
Just create the file /etc/postfix/sasl_password with following content:
Now you have to create the database password file.
Don't forget to restart your postfix service!
The path of the password file can be different. It's your choose.