How can I save or log the email addresses in this form?

Here's the form I am using. When a user input the email address in the form below ...how do I change it so that the email address is saved in a file or mailed to me?

<form action="<?php echo htmlspecialchars($_SERVER['PHP_SELF']);?>" method="post">
<input type="text" name="email" value="<?php echo htmlspecialchars($email); ?>"><br>
<input type="submit">
 
</form>

Code (markup):

 

<form action="<?php echo htmlspecialchars($_SERVER['PHP_SELF']);?>" method="post">
<input type="text" name="email" value="<?php echo htmlspecialchars($email); ?>"><br>
<input type="submit" name="submit">

</form>

<?php
if(isset($_REQUEST['submit']))
{
$to = $_REQUEST['email'];
$subject = 'the subject';
$message = 'hello';
$headers = 'From: ' . "\r\n" .
'Reply-To: ' . "\r\n" .
'X-Mailer: PHP/' . phpversion();

mail($to, $subject, $message, $headers);
}
?>

this is the sample script