It depends on what you are trying to accomplish. If you have a normal
consumer type internet connection, broadband or dialup, through an
internet service provider, you will probably need to set their mail server
as your smart host, relaying all your mail through them like any other
consumer/user.

If, on the other hand, you have a permanent connection to the net,
a fixed ip address and a domain name, your server should be able
to send mail directly to most mail servers on the net, assuming that
the mail is destined to a user on that server

If you don't have a fixed ip address, many servers will refuse your connection
due to increasingly strict spam filters.

Look carefully at the error messages. Are they from remote servers
refusing your connection or is it a firewall not letting you out.