You would have a form that requests the username address of the user via POST. And run something like this..
<?php
$host=""; // Host name
$username=""; // Mysql username
$password=""; // Mysql password
$db_name=""; // Database name
$tbl_name=""; // Table name
mysql_connect("$host", "$username", "$password")or die("cannot connect");
mysql_select_db("$db_name")or die("Error");
$us=$_POST['myusername'];
$myusername = mysql_real_escape_string($us);
$sql="SELECT * FROM $tbl_name WHERE username='$myusername'";
$result=mysql_query($sql);
$count=mysql_num_rows($result);
if($count==1){
$row=mysql_fetch_array($result);
$message = "Your password is {$row['password']}";
mail($row['email'],"Your Password", $message);
echo "Password Recovery Email Sent"
}else {
echo "Error The Data Entered Did Not Match Against Our Database";
}
?>
Not tested but should work.