Is there some special modification that we will need in order to be able to use Google maps on our cell phones while on a driving tour of Italy?

No. The first time you turn it on it might take a bit longer to lock onto the satellite but that's the worst thing that will happen.

It's not a bad idea to download the maps to your phone at home. This will save data when you're traveling. NB the maps expire after 28 days so if it's a long trip you want to redownload them on your hotel WiFI.

That's about it.

Google will not tell you when you might be entering a ZTL in Italy, and will even give you directions to drive into one if you plug in an Italian address that is inside a ZTL. This could result is hundreds of euros in draconian fines for every violation of the law. ZTLs are monitored by video surveillance, and rental car agencies cooperate with police in providing the home addresses of foreigners who break Italian driving laws.

ZTLs are in effect in every major city in Italy and thousands of picturesque medieval villages, many of which are the most popular with tourists. You cannot use Google as you would in many other cities and suburbs outside of Italy. You can't just plug in an address and drive there without regard for whether or not you are allowed to take that route. ZTLs are in effect for some hours of the day or week and not on others, so you need to know that information for your destinations if you want to avoid huge fines.

Maybe I should add that I don't use google maps on a cell phone (I use a dedicated GPS unit when driving), and am not very techie to begin with, so maybe someone with recent relevant personal experience can confirm or correct my information specifically about ZTLs. But using standard wifi on a computer to plot directions via Google maps, I have noticed that Google, when giving directions between Point A and Point B, will at best merely include a vague warning that some of the route it is mapping out has restrictions, but it doesn't tell you where they are. In other instances, Google doesn't even warn. I have experienced it mapping a route that I know from personal experience is within a ZTL at certain times of day, and no indication of that fact in the directions Google is giving.

I don't think any GPS gives out ZTL warnings. ZTL are person/car specific. If you live inside the Rome ZTL you don't have the same restrictions a tourist would. But you're supposed to know the street signs and other relevant rules of the road.

The other thing is most tourists aren't randomly driving from point a to point b. Most have sort sort of plan before they leave home. It's not that hard to check the location of ZTLs before leaving home. Make sure you aren't driving into areas with ZTL.

But getting back to the ZTL. The ZTL is basically a variation of the no entry sign. Missing a ZTL sign is expensive but missing a no entry can be dangerous.

You will find that the street view function does not work in Germany, this is not a technical issue but a legal one.
You would generally do better working with one of the Here apps and down load all the maps before you leave wifi, then just use GPS, it will save on power usage as well as data flow costs

You can do the same thing with Google maps. Here has at times strange routing.

I use Here (we go). I had it on my WIndows phone and when I (reluctantly) moved to Android it was the first app I added. We use it all the time in the camper, but don't blindly follow it, anymore than we blindly follow the built in GPS in the car. I tried Google but prefer Here. There is no time limit on the maps and they update fairly regularly. You can choose to download a whole country, or just the areas you think you wil be visiting.
It's taken me all round California as well as a huge chunk of Europe and the routing never seems that odd to me, and I am someone who also sits with a paper map on my lap!

Anyway whatever app you choose to use download the maps you think you will need, and then some, before you leave home. Turn off mobile internet and use the maps offline. In Here you can choose to use it offline without turning off internet, I don't know about in Google.

We use 'waze' in Belgium and the Netherlands. Has anyone used it in Italy?

And are there good websites that list ZTL zones in Italy?

Waze is a google product like maps. The speed limits in my experience aren't always right. That's the biggest issues I've seen.

You can find the best information for the ZTLs on each cities website. I just noticed Google maps is showing the ZTLs for Rome. Not for Florence. I would still personally go to the city websites and check.

Rome ZTL

For example that's Rome. It's rare for a tourist to need to drive into the centre. Leave the car outside. Or better yet think about the train.

At times both Google maps and Here have strange routings. Which is also true of the pure GPS systems. Using these idiot savants is always a danger

Regarding the first italicized point, it is increasingly the case that many non-Europeans come to Europe and just insert an address into a GPS, and then blindly follow the oral instractions being said to them. Doing that in Italy can be, as you note, expensieve

As to the second point I italicized, an Itlaian ZTL sign actually does NOT resemble a No Entry sign to most North American drivers, -- whereas the Italian "no parking or standing" road sign is very frequently mistaken for a "No Entry" sign by most non-European tourists, resulting in a lot of confusion. Also, many ZTL signs are electronic flashing signs -- and they are flashing the rules in Italian.

The bottom line is that for most places tourists want to go in Italy, driving a car there is not simple and straightforward, and using a GPS or Google maps does not eliminate the need to be sure the specific routes your are taking to a hotel, restaurant or tourist sight are legal. And learn the road signs.

It's dangerous to not know the road signs. It's bad enough risking your own life but risking the lives of the other drivers is worse.

If you're behind the wheel you should be able to read and understand the signs while moving.

The sign you see at the beginning of a ZTL (red circle, white inside) means "road closed to any traffic in both directions".
You must not drive or ride any vehicle, including bicycles beyond that point.
Then you have a list of exemptions which may or may not make you eligible for an exemption of that rule.

The "red circle/white inside" sign is used fairly widespread across Europe, e.g. for residential roads (often exempt for residents and customers of local businesses by additional signage, excluded for through-traffic) or with exemptions for bicycles or official vehicles.

"NO ENTRY" signs look different and are typically found at the wrong end of a one-way street.