What alternative methods can be used to implement user authentication and logout functionality in PHP instead of WWW-Authentification?

Instead of using WWW-Authentication, you can implement user authentication and logout functionality in PHP by using session management. When a user logs in, you can store their credentials in a session variable and check it on subsequent requests to authenticate them. When a user logs out, you can simply destroy the session.

// User authentication
session_start();

// Check if user is already authenticated
if(isset($_SESSION['user_id'])) {
    // User is authenticated
} else {
    // Redirect user to login page
    header("Location: login.php");
    exit();
}

// User logout
session_start();
session_unset();
session_destroy();