Anybody looking for decent pay and holiday pay to boot would be best served giving Italy a miss. It is certainly possible to find work here and contrary to what a previous poster said, a CELTA is not required. Many schools advertise a preference for applicants to hold one, but that's for the benefit of customers who see the adverts. In practice they lok for the cheapest employees.
The largest schools in Milan, for example, have 'training' programs set up for new arrivals. They give you a few hours guidance and then chuck you into the classroom to see if you can swim. Their conracts mean that it doesn't matter if you can or not; if they don't like you they'll simply stop giving you lessons and if you don't work, you don't get paid. Full stop.
Working privately is the solution. I earn somewhere around 2000 euros a month working what amounts to part-time and don't work for a school. I could earn more, but I now choose not to work in Milan itself. I hate the place. However, working privately requires time. Private students don't wait at the train station for new teachers to arrive in Italy. Word of mouth only helps people who've been here for a few years. Schools help themselves. Advertising in papers is prohibitively expensive and the schools dominate internet searches for teachers. In my home town I have 3 different websites on google's first page of search results, but that took a long time to achieve.
As posted elsewhere, we (some friends and I) set up a teacher directory for Lombardia (www.milanoinglese.com
and .it) but this won't help people who want to come here short-term. If you're here short-term, your best bet is to look at the 'summer camp' type jobs. Otherwise, find another country!