One option is setting up real mail MTA or something simpler like msmtp or nullmailer. While this is the preferable, "true unix" way, I think plenty of ordinary linux users don't have this either.
If, for whatever reason, this is not an option, but you have access to another box, where a MTA is set up correctly, you can do this:
- commit the change(s) into the git tree
- create the patch emails with: git format-patch --to to@addr ...
- transfer the produced patch email files to the box where you can send mails from
- send the email(s) with: /usr/sbin/sendmail -oi -t < mail-formatted.patch
The first time I suggest you send the patch to yourself to verify it's all working as expected.
This approach has a downside: You don't see the mails you sent in your MUA sent mail folder. Depending on your MUA, there are other ways of sending the mail. If you're using mutt, you might be in luck. But in general MUAs tend to mangle the patches. :-(