How does one get to the train station in Florence from the airport? Is there a metro or any public transport?
There's a SITA bus. Try THIS LINK to see the schedule. The SITA bus may not go into the train station itself as it's main station is a block away. But, it's very close.
like Larry said. Runs every half hour for E4.50, takes about 20-25 minutes. Leaves from south end of airport complex near main entrance