Wenn E-Mail ein eindeutiger Schlüssel ist, wäre das einfach
<?php
mysql_connect("localhost","root","root");
mysql_select_db("howdini");
$email = mysql_real_escape_string($_POST['mail']);
$sql="INSERT IGNORE INTO newsletter (email) VALUES ('$email')";
mysql_query($sql) or trigger_error(mysql_error()." ".$sql);
if (mysql_affected_rows()) {
header("Location: /thankyoupage.php"); //Redirect page
} else {
//already exists
}