By default, your domain will accept email only to the same address as your tentacle.net username. For example, if you have registered example.com, and your normal email address is email@example.com, then you can only receive mail addressed to firstname.lastname@example.org. This will end up in your email@example.com mailbox just as if it had been sent there directly.
You can add just about any address you like (though certain addresses are overridden, so you can't use postmaster or abuse, for example) as an alias, which will behave the same as above. If you want to change this mapping, you can edit the file in /etc/mail/exim/virtual with the same name as your domain.
In addition to having aliases just to your mailbox, you can set up any number of aliases pointing elsewhere. Using example.com again, you might see something like this:
joeuser: joeuser janeuser: janeuser admin: joeuser albert: firstname.lastname@example.org mildred: email@example.com friends: joeuser, janeuser, firstname.lastname@example.org
Note that leaving off the domain on the portion to the right of the colon denotes a local, tentacle.net address.