La Spezia to Cinqua Terra

It is a local that runs every half hour during the day for 4 euros.... Just buy the tickets at the station.

https://www.lefrecce.it/B2CWeb/search.do?parameter=searchOutputViewer&cFID=WkrFcV10jXaU

Yes, you'll be using regional trains (no seat reservations) so buy your ticket in La Spezia and don't forget to validate it before boarding your train!!! Checks for invalid tickets are common on the CT route, fines are high, and pleading ignorance will not get you off the hook so stamp it and go! :O)

https://www.cinqueterre.eu.com/images/stories/Cinque-Terre-train-timetable.pdf

No italian train needs to be reserved in advance. High speed and Intercity trains rarely sell out, the local trains with no reserved seats can't sell out.

Since you have already bought the tickets for the first leg, why don't you get online also the tickets to Monterosso? Choose a train departing 5 minutes after the scheduled arrival time of the train from Florence. One thing less to worry about on holiday.

Anyway, I would buy in any other Trenitalia station, or in a Tobacconist shop somewhere else in Italy. La Spezia station is often overrun with day-trippers and cruise passengers. Find a ticket machine in Florence, push the UK flag and change the Departure station from Firenze SM Novella to La Spezia Centrale.

A locally purchased ticket can be used on any Regionale train making that route on the picked day. The flip side of these open tickets is that you won't be allowed to take the fast Intercity trains to Monterosso.

Remember that if you forget to time-stamp before boarding, you will be fined on the spot.

Where do you validate the tickets? Also do you recommend buying tickets ahead of time for the local train that runs between the CT towns.

Might I suggest you visit this website: https://www.seat61.com/Italy-trains.htm
There is a wealth of information including videos and lots of pictures about using the Italian rail system.
I read it from beginning to end prior to my two weeks in Italy last year and it was invaluable.

Rick

For future reference, it's a good idea to buy tickets to your final destination. In this case that would be whichever of the five towns you'll be staying in.

I'd suggest buying your tickets before you leave Florence, either from a Kiosk or staffed ticket office. You can buy them anytime, even a few days before you'll be travelling. Just be sure you specify the actual date of travel, as tickets are date-specific. As mentioned previously, be sure to validate (time & date stamp) the ticket prior to boarding the train on the day of travel. Here's a demonstration on validating tickets - https://www.youtube.com/watch?v=rdvRkB7E-sY . The validation machine may also be green & gray coloured.

I'd suggest buying your tickets before you leave Florence, either from
a Kiosk or staffed ticket office.

Backtracking on my previous post advising buying your ticket to Monterosso in La Spezia. Go with Ken's good advice above to buy it in Florence. What can make sense to purchase in L.S. would be one of the combo trail/treno passes if planning to hike any open part of the Sentiero Azzurro/Blue Path + use the regional trains enough to make the card pay off. Otherwise, each ride on the regional trains costs 4 €.

https://www.cinqueterre.eu.com/en/cinque-terre-card

here is a great site that helps explain train travel in Italy and the ins and outs of ticket purchases, ticket machines etc.. https://www.seat61.com/Italy-trains.htm It shows the ticket machines if you scroll down the page a bit and then if you click the right place they have a thorough explanation of how to use the machines. https://www.seat61.com/Italy-trains.htm#Self-service_ticket_machines