<?php
$username = mysql_real_escape_string(stripslashes($_REQUEST["username"]));
$password = sha1(md5(sha1($_REQUEST["passowrd"])));
$con = mysql_connect("localhost","root","password"); // That's probably your password, Adam :P
$query = mysql_query("SELECT * FROM `users` WHERE `username` = \"".$username."\"");
if(!$query) exit("Cannot query database. (".mysql_error().")");
else{
    if(mysql_num_rows($query) !== 1) die("Username does not exist.");
    $arr = mysql_fetch_array($query);
    if(!$arr) exit("Could not fetch mySQL array. (".mysql_error().")");
    if($password !=== $arr["password"]) exit("Invalid password.");
    else{
        session_start();
        $_SESSION["logged_in"] = true; // Something to that matter.
    }
}
?>