Exim4

Tail your mail log
$ tail -f /var/log/exim4/mainlog

Configure exim4
$ sudo dpkg-reconfigure exim4-config

Choose to split up the files.

Choose option: 3. mail sent by smarthost; no local mail

Put the system mail name as your domain hosted (example.com) with DreamHost.

For smarthost entry put in mail.example.com

Edit: $ sudo vim /etc/exim4/conf.d/auth/30_exim4-config_examples

Edit: $ sudo vim /etc/exim4/passwd.client And put in your authentication details.

You can add (if you have problems with encryption): AUTH_CLIENT_ALLOW_NOTLS_PASSWORDS = 1

After the comment section that mentions client side authentication to disable TLS (aka encryption).

It is good idea to have seperate passwords for shell and mail as currently this method sends passwords in the clear.

Test
$ echo testinggagain | mail someone@example.com

And look at your mail log.