There is only one trip each month, mostly towards the end of the month.
They seem to announce one departure at a time. The November departure will probably be listed before the end of October. Check the following web page regularly:
https://www.ferrocarrilcentral.com.pe/reserva.php
This website is useless for booking.
Next departure is on the 29th of October at 7:00AM. The train leaves from Desamparados station, at the end of Jiron Carabaya, a short walk from the Metropolitan Cathedral.
Once in Lima, just go to Desamparados (now casa de la Literatura Peruana) and ask the security lady about the time and date of the next departure. She will also direct you to the place where you can buy your ticket(s). Its is in a shopping mall not far away from there. Don't think there will be any problems with availability, courtesy of low season and high prices. Count on paying ~300US$ pr one-way ticket.