First of all, please note, that coming to Italy with a student visa does not entitle you to work. Your first aim is and should be to finish you academic program. However, there is nothing against having a part-time job during your off-hours from school, as long as you sign a work-contract with your employer and pay the necessary taxes and dues to the government.
Ideally you should try to work here for a non-Italian company, they tend to be more honest. Italian employers may at first appear to be more easy-going about hiring black market employees, but in return they expect high results for their risk, or else they will abuse you. So try to do it legal, get a worker visa from the consulate, get a contract from the employer, and then you will be empowered to argue a b um deal.
For immigration, come clean with the consulate about as much as possible from the beginning, and if you're not sure about anything, keep bombarding them with questions until you get to the bottom of things.
Always try to get the latest official line from your local consulate before you come to Italy. Try to get as much info as possible in writing, get names and signatures, be charming, wise as a serpent but harmless as a dove, and make as many friends as you can in Italy, in high or low places.
One way to start job-hunting in Rome is to contact all the temping agencies in the city to see if any of them have current posts for English speakers on their books. That could give you a foothold here, and of course many temps end up being offered jobs with companies they had been temporarily assigned to. Some of the big world agencies are here, such as Manpower and Adecco, or just go to Google or Yahoo and search for “Jobs in Rome”. You will find several portals which feature jobs-opening throughout Italy.
Also buy 'Porta Portese' newspaper from any news-stand, it has loads of classifieds for employment, (though only on certain days of the week - other days have only 'for sale' or 'wanted' ads. You need to get the 'Work' ('Lavoro') edition.

Also, when you arrive here, see if you can find and buy 'Wanted In Rome' magazine, (available at most English bookshops, such as the Economy Book and Video Center in Via Torino 136. This magazine has classified job ads. Another useful publication is the 'English Yellow Pages' in Rome, available from the same store.
Whether you begin job searching while you're still back at home, or if you wait till you get to Italy, you may wish to start an advance campaign by mailshotting a careful selection of companies in Italy with a well prepared introductory letter written in Italian, together with your CV resume.