Teaching English
Yes there is always a great demand no matter where you go in Italy to learn English from a native speaker. You can enlist yourself with one of the many English schools, teach privately, teach Business English, offer conversational English. No matter what town or city you reside in, English is always in demand. Although you may not like or want to teach English, it is a good way to meet people and network.
In the very early years I taught Business English to a subsidiary of Coca Cola in a tiny town in Abruzzo. If you do this privately you can purchase your own teaching books online or at any good bookstore in Italy. You may decide that it would be easier to work for a private school like the British Institute or similar schools. With internet you can research the top schools in the town you will be residing in and just send them your c.v. with any teaching experience you may have.
Interpreting and Translation
Italy is made up of small and large companies, some family owned and run and others large corporate-like companies, depending on the city you are in. Nowadays all companies do some work with foreign companies and yes the common language is English. So you can get a list of the companies in your town, get a good c.v. and contact each company individually. Hint: in Italy a personal visit is always preferred to receiving a letter through the mail. Plus you don't want to risk your c.v. being trashed by some envious secretary. Sorry but been there, done that. So since image is everything in the bel paese...get dolled up and look as professional as possible, get a good c.v. in hand (translated if possible in Italian) and start visiting each company and tell them about yourself.Many companies exhibit at tradeshows and may need a native English speaker to work the tradeshow with them. These jobs usually pay pretty well, should pay your transportation, hotel, meals and hours working at the show.
You may offer the companies the possibility of translating all comunication they receive and send the customers, suppliers etc and could even suggest handling some clients once you learn more about the company.
Working from Home
Nowadays through the internet one can become creative to find work. There are many publications for instance that pay freelance writers to write about their living in Italy. You can also offer translation services (Italian to English) if your Italian is good enough. You can become an agent or representative for Italian companies wanting to export abroad. Perhaps you have some good contacts in your home country that you can start networking with and start an export business (foods, clothing, shoes, etc.). Ebay is also a great way to earn extra cash. Why not scout Italian companies for their overstock and start putting those items on the internet for sale. Maybe you can even have your own website and just sell off your own site directly from the factories. I think the possibilities are endless.
Employment with an Italian Company
Many ask me how they can be hired by an Italian company. Here things work similarly as in the United States. I would begin if possible to have at least one contact name in the department you are interested in in that company or at least a contact with the company. This will help you get your foot in the door for a first interview. Unfortunately it is very much who you know and not what you know for many companies out here. Luck plays a huge factor too as I was lucky to contact a company at the right time (they happened to be looking for a native English speaker with a MBA in marketing). So you can try cold calling if you cannot get a contact name. The best type of contract to get with an Italian company is called "a tempo indeterminato". This is the most secure and you have the right to all the benefits (sick leave, maternity leave, vacation,etc). Nowadays it is very difficult to get this type of contract so consider yourself lucky if you are offered it. If you are confused about what they are offering you, talk to an accountant (comercialista) that can explain to you exactly what the terms are.
I will be honest that finding serious employers in Italy is not an easy task. My advice is to get as much information in writing as you can about the terms of employment, your responsibilities, etc and talk to as many people as you can about it. Be smart and shrewd and you will not be taken advantage of. Good luck!