Say it's 1865 or thereabouts; late enough that train travel is pretty common in the Western world. I'm a middle- to upper-class individual (so I have the time and money) and I'd like to go from my home near, say, Philadelphia to visit my aunt in Manhattan. I don't particularly care about the precise routes; what I'm curious about is mostly the logistics of planning and initiating the trip: how did you get your ticket? Were trains ever overbooked like modern planes are? Would the ticket be for a reserved seat? Could you check a bag to be carried in a luggage car, or were you responsible for dealing with whatever you took with you? Things like that - I'm really curious about the practicalities of it once train travel was becoming common but before it was routine enough that, say, people were regularly commuting long distances by train.
Clarification: is the Civil War over? I'd presume so, and soldiers returning home are back home?
You could buy either a standard seat, or a cabin in a Pullman for an overnight journey. You would buy your ticket at the train station's ticket window. I don't think they reserved seats, but if they had 50 standard seats, and 10 cabins available, that would make a total of 70 possible passengers. (2 people per cabin). (yes, I get this would effectively be a 2 car train, so not very practical). You brought on your own bag, "checking" in a bag consisted of writing your name on a slip of paper and tying it around the handle of your steamer chest, You would get a claims slip from the baggage master, and handing the freight loader your bag. To get the bag back, you had a claims slip, handed them the claims slip, and you get your bag back.
Also, it depends on your budget. You could buy seats, a cabin, first, second, or emigrant class. It really depends on what your budget is.
As a side note, since 1865 would have seen numerous soldiers returning home, due to lack of air conditioning inside a typical passenger car, many soldiers rode on the roof. Most trains averaged under 40 miles an hour. While studying the 1st Nebraska Infantry Regiment which left Omaha to travel across Missouri from St. Joseph to Hannibal, letters and diaries note several incidents of soldiers falling off the roofs of the cars. One incident in 1861 records a sergeant who died after losing both legs and another the same year where four sleeping soldiers fell off with one fatality. The tracks were often uneven and the ride bumpy and slow. There were no sleeping cars and trains ran all night, so the roof was one option, though not necessarily a safe one.