John, no two trips over the same railroad will ever be exactly the same, there are too many variables. An engineer has to know the railroad, his engine and his train as well as his fireman, conductor, brakemen and the current weather. Most modern steam trains are passenger carriers, a cargo that complains if the slack runs in or out too suddenly. This calls for a different operating style than a freight job.
To answer your question in a general way, when working up hill I let gravity stop the train by easing on the throttle and stopping by stalling at low speed then setting brakes. Drifting down hill is a matter of that famous "feel" and the knowledge that I have to stop in so many feet, am I going too fast, too slow or right in the groove. As to stopping on the level, a small application of brakes on the cars gives enough drag to power to a stop, usually.
I will say nothing about emergency stops as they are not a controlled train handling experience, that is all reflex.