We will be in Florence for a week in September and going to Cinque Terre for three days and onto the Amalfi for a week. We are not planning to rent a car so my question is after taking the train from Florence to Cinque Terre can we go by train directly to the Amalfi Coast or would it be best to go to either Florence or Milan to catch a more direct train?
It's difficult to answer that question without having some idea where on the Amalfi Coast you'd like to go. A bit more information would be helpful.
You can take a train from La Spezia to Roma and then on to either Naples or Salerno. these are all fast or freccia trains. From Naples you can take the CIrcumvesuviana to Sorrento and then on by bus if you are staying beyond Sorrento. Or if you choose to go to Salerno, you can take a bus to Amalfi town and then on to Ravello, Positano, or wherever your end point may be.
On the Amalfi Coast we are staying in Positano.
You can get to Positano via either route that Laurel described above, either: train to Sorrento and bus to Positano OR bus from Salerno with a connection at Amalfi town. Boats can be another option, but run less frequently and may be affected by weather. If you look at Salerno on Google Maps or p. 1130 of Rick's Italy book, you'll see that the train station, bus stop, and boat dock are all very close together, so I think it's a convenient transfer point. See boat schedules from Salerno at http://www.travelmar.it/en/.
Thanks for all of your great information! About how long a trip will this be??
Use the trenitalia website to find train schedules (and prices). Two options:
Select La Spezia to Napoli (you have to use the Italian names). There are 2 options: [A] one train change in Rome or [B] two train changes, in Pisa and Florence. The journey, including transfer time, is from 5-6.25 hours. From Naples, you take the local Circumvesuviana train to Sorrento. The local train runs about every half hour and is really a metro. It will take you 10-15 minutes to get through the Naples station. The local trains are often behind schedule. The journey from Naples to Sorrento takes about 1 - 1.25 hours (some trains don't make all the stops). Then you take the bus to Positano - maybe someone can tell you how often they run.
Select La Spezia to Salerno. There are journeys with 1 or 2 changes that take 6-7 hours. rome2rio.com says it's a 2 hour bus ride from Salerno to Positano or a 50 minute taxi ride. There's also a high speed ferry that takes 1.25 hours, but the ferry is probably not near the train station. It looks like the last ferry is at 3.30 p.m.
Take into account that you'll need to get to La Spezia, probably on a regional train (that may be delayed) from whichever CT town you are staying in.