I am a qmail user & have never used postfix, but what you are trying to do is called a relayserver. I have no idea how to setup postfix but I've just done a little snooping & have found that it has a very complex configuration compared to qmail.
A place that I have used extensively for answers to my qmail issues also has a postfix forum. You can find it here --> http://msgs.securepoint.com/postfix/
I also found this site --> http://souptonuts.sourceforge.net/postfix_tutorial.html
<-- from a Google search of < postfix tutorial >
It looks to me as though you need to add the line:
relayhost = [host.to.relay.to]
to the main config file main.cf. But it also look like there are a number of other config files that postfix uses that also need to be tweaked.
Maybe you will be able to make more sense out of what all this means. Qmail is vastly different to what I have seen of postfix so I don't have a clue!
Good Luck... Post back here if this helps or if you find an answer elsewhere.