What is the proper sequence of actions to help someone who has fallen into the water?

Assuming the person has fallen from a moving boat, shout "Overboard" several times to attract the attention of the steersman. If they are close, throw a life preserver. If there is no life preserver close, without taking your eyes off the subject, point to them as the boat is turned and keep pointing until rescue is imminent. It's very easy to lose sight of a head bobbing in the sea or river. As you draw close, shut down the engine or reef sails to avoid colliding or overshooting, then throw a tethered life preserver or rope even if you know the subject is a strong swimmer or wearing an inflatable vest. People wearing clothing become tired or exhausted pretty quickly, even strong swimmers, so do not rely on them coming to the boat.