"OK, where does it tell me how to legally put out a batter-runner? "
They left that rule out when they reorganized the book about 8 or 10 years ago.
We discussed it here and the Rules Committee was notified of the problem.
They chose not to admit their error by making the correction. Therefore we only call batter-runners out when first base is touched by a fielder in possession of the ball by history and tradition.