sendmail on lan

[Vulpes Velox]

How do I get sendmail to work on the lan?

How do I stop all mail errors from piling up so I can get the daily
run and security check out put messages?

example... from one entitled "Returned Mail: see transcript for
details"

The original message was received at Fri, 14 May 2004 10:00:00 -0500
(CDT) from root at localhost

   ----- The following addresses had permanent fatal errors -----
root
    (reason: 553 5.1.8 <root at v42>... Domain of sender address
root at vixen42 does not exist)    (expanded from: root)