The train schedule and fares can be found at: www.ferroviedellostato.it/homepage_en.html
Use a date within the next 7 days if you are looking at taking regional trains (which may be slower, cheaper, but do not require a change in Pisa). Trains do leave from the main train station SMN and start as early as 4:30 am.
However, trains run throughout the day, so there is no need for an early start unless you want one.
Thanks for your reply Is SMN the main train station in Florence?
What are local DEs
When I looked at the trenitalia website I could only see two morning trains and the second being 7am departure.
SMN stands for Santa Maria Novella, which is the main train station.
If the Trenitalia site shows trains with NA in the price column, this means only that the price is not yet shown on the site. The trains will run. Prices for local (Regionale) trains are never shown more than 7 days ahead, although they do not change.
"DE" stands for "Destination Expert": see the list at right.
Note: If you are actually heading for a village in the Cinque Terre, do not look on Trenitalia for trains to La Spezia. Look for trains to the Cinque Terre village that is your destination. For some journeys, you should change at Sarzana rather than La Spezia.
On a weekday there are currently seven connections from Florence to Monterosso shown on http://trenitalia.it/homepage_en.html between 0535 and 11.28 inclusive. It will be a similar figure for other villages.
I suspect that when using the site you have not entered a time into the appropriate box. If you do not do this, the trains shown will start at the the time you are consulting the site. Click 'next' to move around the remaining 24 hours.Edited: 08 January 2011, 16:26
its possible our friends who were staying in Monterosso did it in reverse and day tripped to Florence
Please read the posts above yours for information on how to get train times and costs.