Starting The Old Steam Engine Trains

How are they started and stop?

The basics…
The (driving*) wheels of an old-fashioned steam locomotive are turned by rods (big, slab-like, rods, often with an I-beam cross section) from the shafts of the pistons in cylinders near the front of the locomotive. To start: open the steam valves to admit steam from the boiler into the cylinders. (Smaller rods between the driving wheels and the valve area on top of the pistons control, and can vary, the setting of the valves: this allows efficient operation at different speeds, and allows the engine to run in reverse by changing when steam is let into and out of the cylinders. There is also a valve inside the boiler: if it is closed, no steam goes to the valves right on top of the pistons. Part of the skill of the engineer was knowing when and how to use which valves to control speed and maximize fuel efficiency.)
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For stopping… Use the steam valves to reduce power. The locomotive has air brakes(**), and the engineer can also control the air brakes on the cars of the train. Coming to a smooth stop involves knowing when to use which steam valves and which brakes.
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Forgive me if I'm saying things you already know, but the wording of your question … could have been by someone who needs to know the ULTRAbasics!
(*) On a typical steam locomotive, the "driving" wheels are the ones that are powered, that provide the driving force for the train. These are the larger diameter wheels, under the middle of the locomotive, connected by rods to each other and to the cylinders. On large locomotives -- locomotives other than switch engines -- there are usually also some smaller wheels near the front. These are called the "pilot" or "pilot truck" wheels: they help spread the weight of the engine, and are connected to the chassis in a way that helps guide the locomotive when it is going around curves. There can be either two or four pilot wheels (that is, either a one-axle or a two-axle pilot truck: three-axle pilot trucks are very VERY, rare). The steam cylinders for running the locomotive are above and between the pilot axles with a four-wheel pilot truck, and typically just behind the pilot wheels with a two-wheel pilot truck. There can also be a one or two (or very, very, rarely three) axle "trailing truck" behind the driving wheels. This supports the weight of the firebox (the part of the boiler where the coal is burned).
(**) The air pressure for the air brakes on the cars of the train is provided by a compressor on the locomotive. All the brakes on all the cars are connected by air hoses, and the engineer can apply or release the brakes from the locomotive cab. These train brakes are called "automatic brakes," since they are, as it were, "remote controlled" from the locomotive. The locomotive's air brakes are separate from this system, and are called "independent" brakes for this reason. In controlling a train -- on hills, or when stopping -- it is sometimes a good idea to have the locomotive pulling enough to keep the train stretched out (you really, REALLY, don't want to "jack-knife" a train!): hence the separate operation of the brakes on the locomotive and the rest of the train.

I hope this is helpful.

I was given a NYC airbrake and train handling book from the early 1900s. At the time, not all the freight cars were equipped with airbrake. The book said to position all of the equipped cars on the head pin. The method was to bunch the slack before and while making an automatic brake application. Most of the rest of the book would still hold water now. All of the brake tests were just about the same.

If some engineer from 100 years ago was able to time travel to now, I think he would fit right in. A few pointers about diesel locomotives, and the modern ABDW control valves, and he'd be off to the races.

On a GE 25-tonner I know well, you start off by releasing the train brakes and the independent brakes, then advancing the throttle until you hear the relays "click". The train will begin to move and you can notch up the throttle to get up to speed, literally feeling (in the seat) the train slack pull out one coupler at a time. Stopping has been well covered in the posts above.

On two 50-tonners I know, you release the train brakes, then open the throttle until it clicks in, then slowly release the independent brake as the slack pulls out. Once moving, throttle up to speed.

The steamers we have are similar, some throttles easier to open than others. Two much throttle all at once can make the drivers slip, and make you look bad. Slipping drivers are a Hollywood thing, not something a competent engineer would do.

Like any automobile, each one is a little different in operation.