The main north-south link, which skirts Florence, is the Autostrada del Sole, which extends from Milan to Reggio Calabria (it is called the A1 from Milan to Naples, the A3 from Naples to Reggio Calabria).
To the north of Florence, the A1 links to Bologna on a busy, winding stretch with lots of tunnels (goes through the Apennine mountains) and to the south to Arezzo and Rome.
The closest exits to downtown Florence are "Firenze-Certosa" and "Firenze-Signa".
Remember that the autostrade are toll roads so you pay depending on how much you have travelled on them. You can pay with credit cards, cash or Viacard. You can purchase a Viacard from toll booths, fuel stations, some banks, tourist offices, and tobacconists.
eta: Nic/Don the only team seen driving in the dark? hmmmm