The closest airport is the Florence airport, about 6 km north of Florence. The easiest way to reach the city center from the airport is by taxi (about 25-30€).
Other airports in order of distance are Pisa, Bologna and Rome. In this case, the best way to reach the city of Florence is by another flight or, better, by train (the Florence main station is Santa Maria Novella).
All the main italian cities are directly connected to Florence by fast trains. The Florence central train station (Santa Maria Novella) is within walking distance to the city center. Train connections can be searched and booked on Trenitalia and NTV websites.
Florence can be easily reached by car. The most important italian highway, the A1 highway, just passes next to Florence.