Florence train to CT May 2019

No you don't need to reserve a train in advance; just buy them locally at the station either from a Kiosk or staffed ticket office. Many of the trains on that route will be Regionale and there are no reservations possible on those trains. Have a look at the Trenitalia website to see all the solutions. I generally look at three factors - departure time, overall travel time and number of changes. You will likely change trains at La Spezia Centrale, but I'd suggest specifying your end destination when you buy the tickets.

One important point to note is that you must validate locally purchased Regionale tickets prior to boarding the train on the day of travel, or you'll risk hefty fines which will be collected on the spot. Also, especially if you're buying from a Kiosk, be sure to specify the actual date you'll be travelling.

No need to reserve anything.
If you want to check schedule look here:
www.trenitalia.com
From: Firenze Santa Maria Novella (Florence Main Station)
To: Vernazza
Date: May ??
Time: 00 (if you want to see all departures leaving from the morning)

There are many options throughout the day, but most involve Regional trains in whole or in part. Regional trains are like commuter trains and no reservations are necessary. You hope on and get a seat in a first come first served basis, just like a city subway.

There is a high speed train that gets you to La Spezia very fast. However that train calls at Firenze Campo di Marte, Florence second largest station, and it departs early (like 7:30am) you could save a bit by reserving that one ahead, but you can also buy that one on the spot. You can see that one on the schedule if you enter FIRENZE TUTTE LE STAZIONI (Florence all stations) instead of just Firenze S.M. Novella.

When traveling on regional trains that require changes, it's common to receive multiple tickets - one for each segment. Don't validate them all in Florence, but rather validate each ticket prior to boarding that train. In Pisa and La Spezia, there will be machines to validate the tickets either on the platform or in the underpass between tracks.

If you don't mind the early 7:36 departure for the direct Florence to La Spezia Freccia train, it's an easy and not terribly expensive cab ride to the Campo di Marte train station. Discounted tickets are still available for the last week of May, but even the full fare isn't expensive (27 Freccia + 4 local).

Thank you all very much for your helpful replies