Finding a Train at the Station

You'll be fine. Termini is easily navigable. Was there last summer and they were funneling all passengers through a central security check on the main floor. If that's still in place, you'll just get through that to the platforms, look up at the departures board, and walk to your train. It's a well marked/signed environment. And the staff are quite helpful. Just leave some extra time to get through security so you're not rushed. And don't linger in the main hall - all the pick pocket warnings you've heard are real. La Spezia will be even easier, as that's a tiny station by comparison.

Awesome. One less thing to stress about. Thanks Steve!

We took a train from Roma Termini last week. No security check, but you had to scan your ticket on a machine to open the gates leading to the platforms for our departing train.

https://www.ricksteves.com/travel-tips/transportation/trains

^^This section of Rick's Travel Tips subforum may be of help

Train stations are really easy to manage. Just arrive a 10-15 minutes before your departure time to get yourself acclimated. Look over the departure/arrival schedule that should be posted on a big poster, probably on a few of the walls. The lighted sign showing arrivals and departures too but only the next few coming up. Make yourself aware of where the tracks are and how to get to them all as sometimes trains will change tracks at the last minute. Once you master one station you'll be set for the rest. La Spezia is a little different from the rest as it has walkways underneath the tracks but otherwise it's the same process. I enjoy traveling in Italy by train. Even with the occasional delays, it's still preferable to me to be dropped off right in the center of the city.

Nothing to stress over but you will need to change trains at least twice between La Spezia and Venezia S. Lucia. Looks like that would be Pisa Centrale and Firenze SNM Novella (that route is shortest and the option I'd choose) or Parma and Bologna.

You could take the 8:16 train out of La Spezia. change trains in Pisa, again in Florence, and arrive Venice 12:34: 4 hours and 18 minutes. If not an early bird, there's a 10:13 from La Spezia that makes the same station changes and gets you there at 14:34: 4 hours and 21 minutes. As that arrival hour is closer to accommodation check-in time, that might be a preferred choice; your room might be all ready for you by the time you've made your way to it. :O)

Pisa Centrale can be pretty busy as it's a main rail hub for the region but isn't super big or intimidating, although train changes here can be short. But by the point in your trip that you'll hit Pisa station, you'll have already taken a train from Rome to Florence, and trains around the CT so will be old hands at it. You'll be fine.

And have a look at the section all about Italian trains on
The Man in Seat 61 website.
You'll find lots of great info with photos of what stations look like.

https://www.seat61.com/

Be sure you are all able to lift your luggage on and off trains....some have two or three steep steps to get from the platform into the train.
Also, at La Spezia you may have to go down and up again on flights of steps to get to your platform, so be sure you are able to do that with whatever luggage you are bringing.
Some stations have elevators, but occasionally they are out of service.

Not much different from finding the right gate at an airport.
When you enter the main hall look for the Departure (Partenze) electronic displays on the large columns (check photo below).
The displays are all over, you can't miss them. Then you will go through the gates pictured below (use the ticket to open the gates, like at a subway station).
https://goo.gl/maps/gjZKdv6jB5x3D23YA

The displays give you the train operator (Trenitalia or Italo) the train type (AV=Alta Velocità or High Speed, IC=Intercity, R=Regionale, RV=Regionale Veloce, or fast regionale) and the train number. The last column on the right gives you the track number (binario).
https://images.app.goo.gl/5j1JFCxWsPBmgEfv9

Once you are on the other side of the gates (which you see on the right of the image below)
https://goo.gl/maps/NvzQDyjN3AznoGnx7
you proceed to the platform your train departs from

Note that at the platform the display will show the final destination of your train, not necessarily Florence (unless the train's final destination is Florence, or FIRENZE S.M.N.). For example in the image above, if you rotate to the left, you can see that at platform no. 6 the train's final destination is MILANO C.LE (Milan Central station), however the train will likely make intermediate stops in Florence and Bologna (some make no intermediate stops). So the important think is to make sure you get the right train number where you have the ticket for. Trains going from Rome to Florence, may have as final destination VENEZIA S.L. (Venice), MILAN C.LE (Milan), TORINO PN (Turin), or even just FIRENZE SMN (Florence).