login.php
<?php
session_start();
if($_POST) {
    $username = trim($_POST['name']);
    $password = trim($_POST['pass']);
    if($username === "admin" && $password === "admin") {
        $_SESSION["authenticated"] = "true";
        header("Location: admin.php");
    }
    else {
        header("Location: login.php?error=1");
    }
}

?>

<?php if(isset($_GET['error'])): ?>
<p class="error">Zlé prihlasovacie meno alebo heslo!</p>
<?php endif; ?>
<form method="post" action="">
    <p>
        <label for="name">Prihlasovacie meno:</label>
        <input type="text" name="name" id="name" value="<?php if(isset($_POST['name'])) $_POST['name'] ?>" />
    </p>
    <p>
        <label for="pass">Heslo:</label>
        <input type="password" name="pass" id="pass" />
    </p>
    <input type="submit" value="prihlásiť" />
</form>

admin.php