This information is from 2008 but should be reasonably useful still.
Most trains and stations are accessible to people with most any disability, but there are some tips to make your trip easier. Also, note that even if you have no disability per se but just have trouble walking around a large station or up and down stairs, some of this may apply to you as well.
Making Your Reservation
Generally, you should inform your travel agent or Amtrak agent of your disability at the time you make your reservation. You’ll want to ask if the stations you’ll be using are accessible, and anything special you should know for your trip. If you are connecting at a large station like Chicago, you’ll want Redcap assistance to get from one train to the next.
Generally, if you have specific needs, you should not make your reservation online.
At The Station
A few Amtrak stations are not staffed; at those stations, crew from the train will assist you when the train arrives.
At other stations, you should check in at the ticket counter and make sure they understand what needs you have. Plan to arrive a little early to make sure there is time for everything.
While trains are spacious compared to other modes of travel, they are still more confining than an average home. Amtrak personnel will help you move about, but you should know that you may not be able to get to all areas on the train, especially if you need a wheelchair to get anywhere. Accommodations can be made; for instance, they may bring your meal to you instead of requiring you to go to a different car.
The equipment that poses the greatest difficulty is the Superliner, which is used on most routes in the midwest and western United States. Superliner trains are bi-level and have stairs in the center of each car for moving from the top floor to the ground floor. Also, crossing from one car to the next is possible on the top level only.
Superliners provide seating (or rooms, if in a sleeper) on both the upper and lower levels, and most restrooms are on the lower levels. People with disabilities will normally be seated on the lower level so they do not have to use stairs to access the restrooms or get to their seats. Sometimes, Amtrak will help you move from one car to the next at a station stop. If you can climb stairs, you will be able to change cars like anyone else.
Most trains provide at least one accessible restroom in each car.
Amtrak tends to be very accommodating to people with disabilities, but make sure to request services and information in advance.
Links to this note
These are generally offered on trains that travel overnight (though you can of course use them during the day as well.) Sleeping car accommodations are considered first-class service, and in addition to the room, you get several other amenities: free meals in the dining car (including everything – even desert – except alcoholic beverages), free morning paper each day, free coffee, free bottled beverages, and the ability to use Amtrak’s first-class waiting areas in major train stations. Each sleeping car has its own attendant, so you also get better personal service.
Amtrak is the only cross-country passenger railroad in the United States. Outside a few regions, Amtrak is usually the only way to travel state-to-state by rail, and is the only regular option for cross-country travel by rail. Amtrak operates the trains, and mostly runs on tracks owned by freight railroads. Amtrak is a quasi-governmental corporation, created in 1971 when the passenger railroads at the time wanted to get out of the passenger business. For more information on the history of Amtrak, see the Wikipedia article on Amtrak.
Generally, I have found train travel to be competitive with iir, bus, or car travel. Of course, the specifics will vary depending on where you are going, when, and on what train. Check out the How to Travel by Amtrak page for information on getting fares online or by phone. Also, there are lots of discounts available.