Car rental

Make sure you have an IDP for each driver (purchased from AAA before leaving home)

Learn the Italian driving laws, paying particular attention to those regarding speeding and ZTLs. Otherwise you risk multiple expensive tickets months after returning home.

AutoEurope is a company often recommended by people on this site. It will give you a choice of local rental agencies and types of vehicles available.

I usually rent through www.autoeurope.com, a broker based in Maine specializing in European car rental. They work with Avis-Budget, Sixt, Europcar, Hertz, etc. (basically the major companies in Italy).

I rent from them every year and I recommend them, however my rentals have always been at least one week, but I presume you can use them for one day only.

With one day only at your disposal you can only visit so much, also considering the time necessary to go to the pick up office and the paperwork.

The downtown offices (near the SMN train station, probably close by 8pm, and maybe close on weekends). The other available location is the airport, where you can return the car even at midnight, but it will take a bit longer (and more money) to get there by taxi or tramway (airport pick ups are generally more expensive because of airport fees).

Auto Europe is good advice, but usually 1 day rentals can be expensive FYI.

Inspect every inch of the car carefully when you pick it up, take good photos and make notes (on paper) of anything that's not 100% PERFECT. Be obsessive about this (allow an hour). Do the same when you return it. Drive it like it was a $100,000 treasure you borrowed from someone picky. Have good insurance, wherever you get it from. Watch out for ZTLs and speed cameras.

International Driving Permit:
It's mandatory in Italy and fines start at 408€ for not having one.
You can get the IDP AAA in minutes for $20 + $9 for photos if you don't have your own.

Road Signs:
Road signs in Italy are based on the International Road Signage system. They are straightforward symbols but take time to become familiar with them. You can read this article.

ZTL or Zona Traffico Limitato (Restricted Traffic Zone):
These areas are present in the historical core of practically every town. The one in Florence is one of the largest. Only residents with permit can enter in those areas. Avoid them. Just park outside the town centers and walk in.
Get a primer on what the ZTL is in this article

Preferential Lanes (bus and taxi lanes):
When you see a lane with a large yellow stripe on the left and a BUS written on the ground, don't use it. It is reserved to buses and taxis. The sign like this one alerts of an upcoming one.

all excellent advice.

Just adding that you also need your license from home. Not just the international one.
We saw a woman denied a rental car last month in Florence because she thought she only needed the international license and left her licencs at home. "Distraught" does not begin to describe her reaction.

A good reminder Dartmouthgirl. Those new to driving in other countries need to know that the IDP is a permit, and not a license. The permit simply assists foreign authorities in translating the license. The two must go together.