If your system cannot relay mail correctly already, as most office setups are easy to configure to be able to provide that without extra config, at least for Linux setups, then the set up means having something like the following in their gitconfig:
cat .gitconfig
# snip
[sendemail]
to = default@list.example.com
annotate = yes
suppresscc = self
smtpencryption=tls
smtpserver=imap.example.com
smtpserverport=587
smtpuser=foo.bar@example.com
(only the ones starting with "smtp" are relevant for mail, the other ones are just there for convenience)
And that has to be done once, iow., in essence it's as hard a setting up an email fat client like thunderbird.
