Staying in touch by telephone
Needless to say, it costs a fortune to make (or receive) calls on a UK or US mobile while in Italy. That said, Vodafone offer their British customers an arrangement called 'Vodafone passport'. This charges an additional connection fee per call, and then reverts to UK rates. See their website for details of that.
For the rest of us, there are plenty of phone boxes and phonecards are readily available. There are also a few internet cafes that feature international calling booths. If you're going to be in Italy for a while, you might think about getting an Italian phone from a provider like Tim or Wind. If you want to go down this route, you will need a codice fiscale. These aren't hard to get hold of and if you catch a shop assistant on a good day they may well sort it out while you wait.
Dialing codes
The international dialing code for Italy is +39 and the code for Rome is 06. The 06 prefix is always used, even when calling from inside Rome.
Skype
An alternative method of staying in touch while you're in Rome is to use a computer program like Skype. You'll need a laptop and a decent internet connection (perhaps through your hotel's wireless network, or by setting up a broadband connection wherever you'll be living). Skype is a free download that allows you to use your computer as a telephone. Calls to other Skype users are free, as is receiving telephone calls on your computer. You can also make calls out, but there is a charge for this (rates vary, but tend to be much cheaper than using a normal telephone). You can buy calling credit in advance from their website.
You can find out more about Skype, and download the software, from the Skype website.
