While you would want to set up a proper email relay on a full-fledged server, for a small home machine, nothing beats the simplicity of having Gmail as the relay.

Just add the following lines to /etc/postfix/main.cf:

relayhost = [smtp.gmail.com]:587
smtp_sasl_auth_enable = yes
smtp_tls_CAfile = /etc/postfix/cacert.pem
smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd
smtp_sasl_security_options = noanonymous
smtp_use_tls = yes

Copy Thawte Certificate Authority to Postfix's CA file:

# tee -a will append contents to file if file already exists
cat /etc/ssl/certs/thawte_Premium_Server_CA.pem | tee -a /etc/postfix/cacert.pem

Then generate a Gmail App Password to create the sasl_password file by going to App Passwords on your Google Security tab.

Once you have it add the following line to /etc/postfix/sasl_passwd:

[smtp.gmail.com]:587    [email protected]:APP_PASSWORD

You must then fix sasl_password permissions:

chmod 400 /etc/postfix/sasl_passwd

And then use postmap to generate sasl_passwd.db file which postfix will need:

/usr/sbin/postmap sasl_passwd

The only thing left to do is to restart the service:

/etc/init.d/postfix reload

You can then use this one-liner to send an email to yourself and check if Postfix is working as intended:

echo "Test mail from postfix" | mail -s "Test Postfix" [email protected]

The logs should show something like this (notice the relay server):

Jun 25 17:14:56 AEC1E9C0043: uid=0 from=<wasteofserver>
Jun 25 17:14:58 AEC1E9C0043: to=<[email protected]>, relay=smtp.gmail.com[173.194.76.109]:587, delay=2.2, delays=0.06/0.01/1.4/0.73, dsn=2.0.0, status=sent (250 2.0.0 OK  1624637698 v5sm11709310wml.26 - gsmt
Jun 25 17:14:58 AEC1E9C0043: removed

Alternatively, you can also check your Gmail "sent folder". As the email will be sent by Gmail using your account, the email will be there.