Train from Milan to Manarola

Consult:
www.trenitalia.com
(select English language by clicking on the icon)
enter from MILANO CENTRALE
to: MANAROLA
Choose a date within the next 7 days (schedules for regional trains go only as far 7 days in advance)
Choose the approximate time (or a little before) the time of your departure from Milan.
Click on search and you'll receive a lot of solutions for your travel.
Since Manarola is a small station all options will require at least one change, generally in Genoa or some other town along the route (e.g. Sestri etc.)

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If you're concerned about changes there is one direct departure from Milano Centrale to Manarola, departing at 07:25 and arriving at 11:14 (time 3H:49M). If you'd prefer a slightly later departure, the next easiest departure is at 12:10, arriving at 15:35 (time 3H:25M, one change at Sestri Levante). There are other trains with two changes and differing travel times. Use the website that Roberto listed to find the train that best fits your preference.

Changing trains often involves disembarking from the train at the intermediate stations, dragging your luggage down a stairway and through a tunnel (Sotto Passagio) and dragging it up another stairway to the next platform. Many smaller stations don't have Elevators, so keep this in mind. Validation machines seem to be in the tunnels these days, so don't forget to validate your ticket if required.

One important point to mention is that if any of the trains you use are Regionale, you MUST validate your ticket prior to boarding the train on the day of travel, or risk hefty fines which will be collected on the spot! If any of the trains you're using are "premium" trains such as the Freccia or InterCity that have compulsory reservations, you MUST only board the train specified on the ticket or again, hefty fines. Reservations are specific to a particular train, date and departure time, and will be included if you buy P-P tickets.

Happy travels!