This is a simple one, similar to defaulting to accept mail locally, by default postfix will only send mail to local recipients.
- Install the necessary packages
- yum install postfix
- Edit the /etc/postfix/main.cf file
- Find the relayhost section and add a line relayhost = 192.168.10.1
- Restart the service
- service postfix restart
You should be able to test this by sending an email to a remote user.