Seems like sendmail is not configured on your server.
What you can do though is to create a mail account on f.e. gmail,yahoo mail or similar and use Zend_Mail to send mails from this account using SMTP.
I took this code example from the Zend Framework documentation:
$config = array('auth' => 'login',
'username' => 'myusername',
'password' => 'password');
$transport = new Zend_Mail_Transport_Smtp('smtp.gmail.com', $config);
$mail = new Zend_Mail();
$mail->setBodyText('This is the text of the mail.');
$mail->setFrom('[email protected]', 'Some Sender');
$mail->addTo('[email protected]', 'Some Recipient');
$mail->setSubject('TestSubject');
$mail->send($transport);
This doesn't require sendmail to be configured as you are using a preexistent mail server that allows smtp.
UPDATE:
As toto pointed out it can be possible that SMTP is also blocked by your hoster. In this case you can try to use SSL by simply adding two entries to the Zend_Mail config which then should look like this:
$config = array('auth' => 'login',
'username' => 'myusername',
'password' => 'password',
'ssl' => 'ssl',
'port' => 465);
Hope this helps.