Hi Daniel,
first: the Internet is not the WWW although many people see them as the
same. They are not.
> I have installed qmail and everything seems OK except for sending mail out
> to the WWW. If I remove/rename the rcpthosts file I can then send mail out
> to any domain, but I presume this is not the correct way to solve this.
Do you use ucspi-tcp (tcpserver)? If not, you should do so and set the
RELAYCLIENT environment variable for your internal network.
This is explained in Dans FAQ, see
http://cr.yp.to/qmail/faq/servers.html#tcpserver-smtpd and
http://cr.yp.to/qmail/faq/servers.html#authorized-relay
Regards, Frank