You should check Laravel 4's documentation on authenticating users, which can be found at:
http://laravel.com/docs/security#authenticating-users
Basically you can authenticate a user by passing $data to Auth::attempt(). Pass true as the second parameter to Auth::attempt() to remember the user for future logins:
$data = Input::all();
if (Auth::attempt($data, ($data['rememberme'] == 'on') ? true : false)
return Redirect::to('result');
else
{
$message_arr = array('message' => 'Invalid username or password!');
return View::make('signup', $message_arr);
}
You should use Laravel's method for authentication, as it takes care of password reminders and more.