Once you exit the airport turn right and head towards the back end of the airport where all the taxis line up to pick up new travelers. Depending on where you are going, it will vary in cost. The taxi drivers are good about getting you to your destination as soon as possible. The taxi drivers don’t expect a tip but a tip is always welcome.
If instead you would rather take the bus from the airport to the SITA bus station. The bus leaves the airport from a stop where you it is clearly marked to right as you exit the airport. You will arrive at the SITA bus station which is right next to the main train station (SMN station) where you can easily walk to the center. You can buy the ticket on the bus for €5.00. The bus leaves every half hour from the airport. The schedule is here.
The taxi option is always my choice when I arrive at the airport. It will take you right to your destination or close to it if it is located on Via Tornabuoni,in Piazza Pitti, or near Via Por Santa Maria. In these cases the taxi will find the closest point to drop you and your luggage and you will have to walk to your hotel. It shouldn’t be too far either. As I said, Florence is small.