This module uses git://github.com/abraham/twitteroauth.git and provide an easier workflow for Twitter OAuth without many extra steps.

return array(
  'consumer_key' => 'get it from dev.twitter.com',
  'consumer_secret' => 'get it from dev.twitter.com'
);

$twitter = Twitterauth::factory()->init();
if (!($user = $twitter->getUser()))
{
  // Not logged in or not authorize, send them to the authorize APP url
  HTTP::redirect($twitter->getAuthorizeURL()));
}
else
{
  // $user->screen_name
}

Done. The redirect should happen in a popup, since the callback calls window.close(). The module takes care of the cookies and session variables for you. If you want, overwrite the original Controller_Twitterauth_Index controller so you can control the denied / errors by yourself (currently it simply ignores it) or even override the callback Route using Route::set('twitter-auth', 'your-route')