session_start();

if (isset($_POST['login']) && isset($_POST['user'])) {
    $_SESSION['user'] = $_POST['user'];
}
if (isset($_POST['logout'])) {
    unset($_SESSION['user']);
}

if (isset($_SESSION['user'])) {
    echo 'you are logged in as '.$_SESSION['user'];
    echo '<form method="post" action=""><button name="logout">Logout</button></form>';
} else {
    echo '<form method="post" action=""><input name="user" /><button name="login">Login</button></form>';
}