In almost all cases, Amtrak seats are not assigned. The exception is Acela Express route seats and business class seating on the Northeast Regional, Carolinian, Palmetto, and Vermonter.
Otherwise, Amtrak has a first-come, first-serve seating policy for coach seats. Essentially, you board the train and look for open seats in the coach or quiet car. If you are traveling with a large group, you can look for the Amtrak “red cap” service desk or staff wearing red caps who can help you find seating. Be sure to tip and connect with the red caps before your train arrives.
If you have booked a roommette or bedroom, you’ll receive your room assignment after booking your tickets.
Amtrak Guide 