Most usual way is get find article and check it $article.user_id = Yii::app()->user->id. Of course, you should allow only authorized users to access for this action.
Second way is use wacf extension and configure resource filter:
public function accessRules()
{
return array(
// allow edit only to article owners
array('allow',
'actions' => array('edit', 'delete'),
'users' => '@'
'resource' => array(
'model' => Article::model(), // specify resource model
),
),
...
);
}