I'm no expert but...
Depending on what email app you use...
In my email app (Sylpheed) I made a user profile or account that gets mail from
root@linux.local
and I tell it that the local mailbox is /var/mail.
I have had some trouble figuring out how to get, in my inbox, all the mail from e.g. root, cups (the print server) and HylaFax (a fax server).
I have another email 'account' where I collect messages from
my_user_name@my_system's_name.localhost
The mailbox for that is also /var/mail.
And one for
root@my_system's_name.localhost
also in /var/mail.
Of course you can also just go to /var/mail and read the messages with a text editor. But it is nicer to pick them up with your usual emails. I have Sylpheed set to "Get mail from all accounts" or some such option.
Good luck.