If you hold a European Union passport you may legally work in Italy although you still need to apply for a work permit (permesso di soggiorno per lavoro) and a residence permit (permesso de soggiorno).
You will need to go to the main police station (Questura Centrale) where you are living to apply for these permits. The Questura Centrale in Rome has a foreigners section with some staff that can help in English. Once you have your work and residence permits, then you will also need to get an employment number from the tax office.
If you don't have an EU passport, then things are much more difficult if you want to do things by the book. However it isn't too difficult to find work under the table especially if you are working for a small business or teaching English.
You could try some classified ad papers including Wanted in Rome (websitewww.wantedinrome.com).
