Networking :: Send Email To Mail Server / Account On Local Network?

I'm trying to configure postfix so smart daemon can send out notifications emails. My system will need to send emails to a mail server that is on the same local network. I have not had much luck in getting this to work, and am confused on what I need to setup to do this and how to set it up. Does my system need to be apart of the same domain as the mail server? If so, how do I do this? Is there any restrictions sending emails from the command line as the root user? Do I need to configure a relayhost?

Basically all I need to do is send emails to a local mail server, i.e. a mail server on the same local network. I do not need to receive emails. I am rather clueless as to how to set this all up, and what I need for this basic email functionality. I have read and tried many postfix configuration tutorials, but when I try to send out a test email to a email address on the local network mail server I always get "Connection refused" to the server and deferred or bounced status on my test email.