The airport is really close to town, a taxi ride is economical at atound 25 Euros (I did it the opposite direction in November 2016). I'm not normally a big proponent of taxis but it worked great. When you pick up your guidebook I am sure they will list public transit options too (I understand you may not have gotten that far in your planning, but your trip is just days away so it's time for that step!)-there is surely a bus and the bus station is very central in Florence.
Addendum: From Rick Steve's Italy 2016: Shuttle buses (to the far right as you exit the arrivals hall) connect the airport with Florence's train and bus stations. (2/hour, 30 minutes, runs 5:00-23:30, 6 Euros). Sounds like it could not be easier!