Cristine,
As the others have mentioned, there are LOTS of trains on that route every day, and travel by train will provide the most "timely manner".
Which "train schedules" are you looking at? If the schedules for September aren't displaying now, just check a day within the next week or so, on the same day-of-the-week that you'll be travelling and that should provide a good idea. The schedules likely won't change much between now and September.
Travel times between Monterosso and Pisa Centrale vary from ~1H:13 - 2H:08M, depending on which train you choose. There are a few direct trains (no changes) that take about 1H:18M. Some of the trains on that route will be InterCity (reservations compulsory) and some will be Regionale (no reservations but you MUST validate your ticket prior to boarding the train on the day of travel, or face hefty fines).