Mail to internet from 10.3 mail program?

Hi,
I’m a complete novice when it comes to mail, sendmail, etc. I have mediawiki running and want it to be able to send e-mails. For this I need to get the php mail() function working. For this I need to get mail/sendmail working (at this stage I don’t want to use PEAR).

So - when I use the mail program, I can send mail between users on the same machine, but when I try to send to the internet (name@domain.com) nothing happens - not even a “Cannot deliver” message. Should this just work out of the box? What could be the problem? Firewall? Further configuration missing? Is it waiting somewhere in a queue?
I have searched high and low but have had trouble finding something between very simple (“just write mail() into PHP”) and very complex.

If someone could point me to a step-by-step guide or something, that would be great.

Thanks
FMc