Trains to Lucca from Florence

Look into the trenitalia.com website for timetables and prices.
Use station names in Italian. For Florence use FIRENZE SANTA MARIA NOVELLA. For the other cities you mentioned use AREZZO, LUCCA, CORTONA-CAMUCIA. As a date use a date in the next week. For time enter 00, so you will see all trains starting from early morning. There are lots of Regional (commuter) trains from Florence to any of the destinations you mentioned. Lucca has good and fast bus options too.

Elsa, It's very easy to travel to the locations you mentioned by train, and that will usually be the quickest method. The links that Roberto provided will give you all the details. A few comments on each..... > Lucca - the station is outside the walls of the city, but it's a very short and easy walk to reach the city centre. You'll see the walls and gateways when you step outside of the station. > Cortona - the Cortona-Camucia station is at the bottom of the hill, so you'll need to take a Bus or Taxi up to the city. If there's no ticket facilities open in the station, you'll need to buy a Bus ticket at the nearest Tabachi. The Bus will stop in Piazza Garibaldi, and it's an easy walk from there to Piazza della Reppublica and other parts of the city. For the trip back down the hill, there's a Tabachi just downhill from the bus stop. I don't have any information on Arrezzo, so can't provide any comments. Travel to those locations will likely be via Regionale trains, so DON'T forget to validate or you'll face hefty fines! Cheers!

From Florence to Arezzo is a short, regional train ride. The train is slow and makes numerous stops, but still took less than an hour. I definitely recommend Arezzo for a day trip from Florence.