First, unchecked Allow people to post comments on the article on the Options > Discussion panel. This will only disable comments on future posts. Now, to completely disable comments, you will have to edit each past post and uncheck Allow Comments from the Write Post SubPanel. Alternatively, you could run this MySQL query from the command line on a shell account or using phpMyAdmin: UPDATE wp_posts SET comment_status=”closed”;

If your goal is to permanently disable comments, then you should delete the wp-comments-post.phpfile as well.