The Florentine, Florence's English language monthly, reports that the T2 tram line between the airport and SMN opened on February 11. The tram will run from 5am until after midnight, and the ride is scheduled to take just over 20 minutes. It appears a standard 1.50 euro transit ticket gets you to or from the airport (or you can ride for free until February 24).
Here's the website. https://www.gestramvia.com/orari