In Italy you must always dial the area code AND the telephone number, even if you are placing a call to someone in the same city. If you call Italy from overseas, you should dial the country code (39), the area code (complete with the initial '0'), and the number.
All Italian residential (fixed) telephone numbers start with a "0", and have between 8 and 11 digits (area code+number).
Cell (mobile) phone numbers have three digit prefix, all starting with a "3", and a 6 or 7 digit phone number. Calls to cell phones from land lines (such as in hotels) are significantly more expensive than calls to other landlines.
Italian toll free numbers start with an "8" and have normally 9 digits, e.g. 800 111 222 (the exception being a few numbers having only six digits, e.g. the Italian Post office info line is 803 160, the Italian Automobile Club roadside assistance is 803 116). To use those numbers, which are often toll free also if calling from cell phones, just dial the number as given, without any additional prefix. Some phone numbers that begin with an "8" are fixed cost or reduced cost calls, but not completely free.
If you have to make an international call to the U.S., dial: 001 + (area code) + (number). That includes if you plan to call an American cell phone number, regardless of where that cell phone may be physically located. WARNING: It may be impossible to call a 1-800 U.S. telephone number from Italy even if you're using an international phone card to call the U.S.
If you have to make an International call to another European country (e.g. France), dial: 0033 (or other country code) + (area code) + (number).
Other option is to rent a cell phone before your departure, with a local line from Italy, you'll have the benefit of low calling rates, including incoming calls free of charge. You'll find several companies offering this kind of service, be aware of those that use call back since the voice quality is very poor. Some good options are www.cellularabroad.com http://www.phonerentalusa.com, www.worldcell.com and www.planetfone.com. Cellular Abroad's solution is specifically geared toward Americans and Canadians traveling to or living in Italy and they have the best rates for calling back home. Rebelfone & Brightroam offers lowest call rates on Italy sim card. Brightroam offers a data package at $149/mo for 5 GB, and Brightroam Voice Plans provide a low calling rate of $0.20/minute in Italy and back to Canada and the USA.
Also, if your phone is unlocked, you can always opt for a local prepaid SIM which can be used even for international calls, in order to avoid expensive roaming fees. Still, if your cellphone doesn't support other carriers, except the one you bought it from, you can unlock it using an online provider, like www.sim-unlock.net or www.unlockunit.com.
Pre-paid telephone cards to be used to call from payphones can be bought at electronics shops, tobacconists' (tabacchi), newsstands and bars. Public phones, however, are becoming less and less widespread: as you will notice, Italians are addicted to mobile phones. You can rent a mobile at major airports, although many long term visitors choose to buy a cheap cell phone for less than 80 euro and a pay-as-you-go SIM card from one of the three cell phone providers (TIM, Vodafone and Wind). You can also purchase this type of solution prior to your departure.
Italian directory assistance is available on ELENCOSI or www.paginebianche.it
Italian white pages are availbles at TUTTINUMERI.IT or www.tuttinumeri.it
Italian yellow pages are available at PAGINESI or www.paginegialle.it
For people from the United States: If you choose to use the payphones in Italy, do yourself a favor, if you only speak english buy an AT&T or whatever calling card in the U.S. Make sure it has lots of minutes, and use the 800 access number for Italy. ( You can get that by calling the company before you leave the states). Telephone operators in Italy may not speak enough English to help you place a call. Please note that many payphones however either do not work or are broken. Italians very rarely use payphones as Italy has the highest cell phone per capita rate in the world.
If you plan to travel for a long time in Europe and need a phone your best bet is probably buying a new or used tri-band or quad band phone on Ebay, Amazon, Cellular Abroad or some other site an Italian sim card.
If you are from the UK and visiting Italy it could be worth it to buy one of 3's PAYG Sims. Three website /Pay_As_You_Go_Price_Plans. They are now using the same roaming rates abroad in 11 countries as they charge in the UK, ie 3p a minute, 2p for texts and 1pm per MB data. Check out their website.