I spend a lot of time talking about Florence's archaic driving zones - the dreaded ZTL - because I think many of the complaints about it are somewhat unwarranted. But this one, the "Corsie riservate" is sort of bogus, since they are usually not that well posted and really do "fool" foreigners (and Italians). I am posting the map below in response to a TripAdvisor user who did their homework, thought they had it all right, and still got a euro 100 plus ticket once back home in the states. You CAN NOT drive on these roads, ever (ever meaning whenever the sign says you can't - I don't know for sure if this is a 24/7 thing or is based on specific hours). The "Corsie riservate" are different from the ZTL so you just need to know about them. If you are coming from the south - Chianti, Siena, etc. and heading into Florence on the via Senese, you need to bear right where you see the red circle, drive up the via del Gelsomino, and then turn left at the traffic light (second light I think) and down the Poggio Imperiale to the circle at Porta Romana. Basically you can stay on that dotted gray route (which is not exact but close - follow the blue and white arrow one way signs!) and come over the ponte Vespucci, hang a right, through the ZTL (which you can enter since you are in a rental car and returning it), left at the piazza, and left again onto borgo Ognissanti and to the various rental car places (or if you rented from Avis and Hertz you can just go straight once over the bridge). In theory you can enter the ZTL anywhere as long as you go right to the rental car place - I provided the gray dotted route as an example and because that entrance is the closest one to most of the car rental companies. In any case - just pay attention, and don't drive through any signs with a red circle until you stop and read them first!
See this map, click on "Mobilita" in the left hand column, and then chose the controls you want to see.