Hi,
well, in Flash you may use the LoadVars Class to handle, send and receive variables...in PHP, let's say that you are using the "POST" method:
<?php
$mail = "youremail@mail.com";
$subject = "Flash Form";
$message = "This is your message:\n";
$message .= "And here goes the variable for the name:".$_POST['variableNameFromFlash'];
mail($mail,$subject,$message);
?>
This is the most basic PHP processment...from here you can go to include HTML, Uploading Files, everything you do on a email application really.
Let me hear from you about this stuff....
Cheers