By train. See www.trenitalia.com clicking the UK flag first for English, and entering your 'hour' of departure e.g enter '13' for 13.00 to see times and costs. Costs for journeys entirely by Regional trains are shown only up to seven days in advance, but fares don't change for these.
From Firenze S M Novella to Monterosso (no 'al Mare' on the Trenitalia website) the route is always the same, but there is a choice of change stations depending on departure time, so simply enter those stations on the website which will then give all the options. The simplest is a Regional train to Pisa Centrale then an Intercity train with reserved seats direct to Monterosso. Or there is travel by Regional trains al the way, with changes at either Sarzana or at Pisa Centrale and at la Spezia Centrale. An expensive method which is sometimes faster but seldom worth the increased cost uses Frecciabiance or Intercity trains with reserved seats between Pisa and la Spezia, and otherwise uses Regional trains.
Enter Monterosso to Siena for similar results. The fewest changes are two, at Pisa and Empoli, but usually three changes are required.