To send emails using PHP you have a few options:
Option 1: Use SMTP
You'll need to modify your php.ini configuration file (http://php.net/manual/en/ref.mail.php) and set the SMTP value to an external SMTP server you can use. SMTP servers are not part of the Windows Azure features at the moment.
[mail function]
SMTP = mail.mycompany.com
Option 2: Use sendmail
You'll need to modify your php.ini configuration file (http://php.net/manual/en/ref.mail.php) and set the sendmail_path value to the sendmail executable.
[mail function]
sendmail_path = "C:\wamp\sendmail\sendmail.exe -t"
Since sendmail doesn't exist in Windows, you'll need to use the fake sendmail for windows: http://glob.com.au/sendmail/
Option 3: Use a mail/smtp service
You could use a service like SendGrid to send your emails (they have an offer for Azure users: http://sendgrid.com/azure.html). They'll take care of sending out the email, you'll just need to call the REST api:
$sendgrid = new SendGrid('username', 'password');
$mail = new SendGridMail();
$mail->addTo('foo@bar.com')->
setFrom('me@bar.com')->
setSubject('Subject goes here')->
setText('Hello World!')->
setHtml('<strong>Hello World!</strong>');
$sendgrid->smtp->send($mail);