There are three main ways you can get a vehicular fine in Italy:
1. Speeding: A few years back, very reliable, inexpensive road-side speed monitoring camera systems were put on the market. These photograph the driver and the car license plate, and record the speed and location of the car. Where previously traffic police had to be in place and to be paid to catch traffic offenders, this can now be done automatically with, in Italy (and elsewhere), an almost 100% acceptance by the courts should the evidence be challenged.
2. Parking: In most cities, parking is restricted to designated lots or to areas where the curb has been painted blue. In either case, you will find a machine nearby called a parcometro. These machines are very easy to use. You decide how long you want to stay, deposit the right amount of coins, get a printed ticket and display it on your dashboard (inside the car). So please have plenty of coins on hand at all times.
3. Entering a pedestrians-only area: Most Italian cities are not adapted to huge volumes of vehicular traffic and efforts have been made one way or another to reduce this volume. In Florence and Pisa (and many other towns) there are a number of zones covering the historical and hotel district where only cars with special permits may enter. Often these areas are delineated by a sort of "border crossing" that you pass through, with the tell-tale camera attached. The cars rented out by car rental agencies do not have these permits. You must therefore take the necessary steps to obtain an exemption each day you drive to your hotel within a restricted zone. Please ask your hotel about this exemption.
In Italy, the authorities have up to one year after they have obtained the offender's details to issue a traffic ticket to an offender in a foreign country (unlike in Germany, for example, where there is a three month limit)! Italian bureaucracy being what it is, the ticket usually does take a year or more to arrive. The recipient of the ticket has 60 days to pay or appeal. If you don't pay, the amount is doubled. Italians usually pay and then appeal.
If you see a bill on your credit card statement but haven't yet received a paper document regarding the fine via "physical" mail, don't worry, you will receive it in the upcoming months. Once you receive the document you generally have 30 business days to pay the fine, or contest the fine. The information regarding contesting the violation will be provided on the document you receive from the Italian authorities. According to article 3.C of the General Conditions of the Rental Agreement, whenever there is a request from any Police Authority for information on the driver renting the car (personal information) or when the supplier has to handle a fine, the supplier charges a fee for administrative costs (e.g. paper work, postage, paying the fine up front for clients so they don't get an extra fee for not paying fine on time etc).
This information regarding the application of this cost appears at every car rental counter in Italy.
Car rental agencies are obliged to and always do provide the traffic authorities with the name and address of the individual who rented the offending car. They charge the credit card of the renter a significant amount of money for doing this - sums ranging from 16 up to 50 euros have been mentioned. In some cases car rental agreements allow the rental company to pay the fine and charge your card for the fine. There is always an additional 20% sales tax (IVA) and there can be hefty late fees as well. Note that in some cities (such as Florence, Bologna and Rome), the traffic authorities request the renter's information via an electronic system where the reason for the request is not specified. You will be charged for this information transfer. It is likely but by no means inevitable that a fine will follow.
The amount varies (35 euros for parking in the wrong place at the wrong time, 150 euros for speeding - that kind of thing) but will surely cost less than any challenge you might mount. If you were en route to or from your hotel in a restricted zone and received a ticket from a traffic officer, discuss it first with your hotel. But if you were photographed doing the same thing and receive the ticket months later, it's probably too late to do anything except pay.
NOT to pay a fine that is sent directly to you at your home outside the EU is probably a bad idea. If you don't pay, the rental company will eventually pay the fine plus the late fees and pass that on to you via your credit card company. There is also evidence around that a debt collection agency called EMO ("European Municipal Outsourcing") is following up these fines quite aggressively.
Note that it won't help for you to cancel your credit card when you return home. The date on which you signed your rental agreement and gave your credit card details to the rental company will predate your cancellation and the car contract will still be honoured by the credit card company who, one way or another, will extract this money from you.
Regarding fines paid by the rental car company and charged to your card: neither your card company nor the car rental companies will assist you unless you can prove that it was not you driving the car, or that you were nowhere near the area and that it was therefore not your rental car! You are assumed guilty unless proven otherwise (as with traffic offenses world-wide). Many municipalities provide access via their web sites that enables you to see the relevant photographic and other evidence, if they do not send it to you, or if it's not you in the photo then it would be wise to contest the fine. The web site and information regarding use of the web site is as follows:
You will be provided a username & password when you receive the actual fine from the Italian authorities. You will be able to not only pay your ticket online, but you can click the download photo link that will be on the page once you log in, and you can see yourself committing the violation. The license plate, car, date, and time will all be on the photograph.
As always, it is best not to get a ticket in the first place, so please try to be aware of speed limits and parking regulations, and be on the lookout for pedestrian-only areas. If you keep your eyes open, you'll have a wonderful, fine-free vacation in Italy!
European Road Signs and Conventions