How do I set up CiviMail on Wordpress CiviCRM plugin?
I would recommend testing if you have sendmail configured properly on your server by trying to send from the commandline (http://tecadmin.net/ways-to-send-email-from-linux-command-line/). Follow general sysadmin approaches to solve that problem, not least of which is to get the ISP support to help you. Once you know your sendmail is delivering from the commandline, you will want to make sure that the PHP run by Apache or Nginx for this site is using the same sendmail.

Hope these pointers help. Sorry it isn't a step-by-step recipe but OS environments vary significantly.

Another alternative worth exploring a bit before going too far down the rabbit hole of setting up sendmail on the server is whether one of the other mail sending options available on that CiviCRM page works.