There seem to be a number of people searching for how to do this, and from what I can see there's very little quick and easy documentation on the net. You've got a server, hosting a website (for example) for example.com.
You want the server to accept mail for example.com but to automatically pass the mail onto a different address.
Assuming you're running Postfix, it's as simple as the steps below
First we make sure the virtual mappings file is enabled
# Scroll down until you find virtual_alias_maps
# Make sure it reads something like
virtual_alias_maps = hash:/etc/postfix/virtual
# We also need to make sure the domain is enabled
Save and exit, next we add the aliases to our mapping file
# Forward mail for email@example.com to firstname.lastname@example.org
Simple! And if we want to send to two different addresses at once, we just specify them
email@example.com firstname.lastname@example.org email@example.com
Finally, we just need to create a hash (actually later versions of Postfix don't require this)
It's exactly the same principle as passing mail into a local user's mailbox.