If you are using Ubuntu and it seem sendmail is not in /usr/sbin/sendmail, install sendmail using the terminal with this command:
sudo apt-get install sendmail
and then run reload the PHP page where mail() is written. Also check your spam folder.
This is probably a configuration error. If you insist on using PHP mail function, you will have to edit php.ini.
If you are looking for an easier and more versatile option (in my opinion), you should use PHPMailer.