I usually board at Chemult, Oregon, an unmanned station, so I have some personal experience with this. I have arrived at the station both by personal car, and by Amtrak-operated shuttle bus. If I'm on the shuttle bus from Bend, it's super easy. The bus driver is in contact with the conductor, and knows exactly when the train will arrive (even if it is late). If the train will be late, the driver takes us to a local truck stop to hang out, and then collects us as soon as the conductor calls him/her to let them know the train will be arriving soon. They then take us across to the platform by bus, and help get everyone onto the platform, and wait with us till the train arrives (as there are often de-training passengers for the bus as well).
If I arrive by personal car, it's very handy to have checked the Amtrak site at the latest possible moment before getting in the car, so I know roughly how late the train currently is. Then I just have to go up the ramp to the platform when I expect the train. It helps if I've seen the shuttle bus arriving!! I've only left my car there once, as the shuttle bus proved to be lots more convenient and I never had to worry again about finding my car buried in snow upon my return (it's usually winter when I have time to travel, ha, ha!).
Since you've bought your tickets in advance, they know you will be boarding. The train will stop, and one or two doors will have attendants or the conductor hanging out the window. They'll open their doors and announce coach and sleeper passengers, and which car to go to. They will only open up the doors for cars that are boarding, and they will make sure everyone on the platform is expeditiously taken care of, then off you will all go.
I am lucky, there is only one Amtrak train in each direction per day at Chemult. It is always the Coast Starlight.