Yes, this is a frequently asked question, so do read the prior threads, which will have lots of tips. You're right, apparently awareness of celiac disease is very high in Italy, since the incidence of it is also high.
My main tip is not to think of gluten free restaurants - you're very unlikely to find these. Instead, look for gluten free items at restaurants, gelaterie, bakeries, pharmacies, etc.
Yes, pharmacies. As indicated in this New York Times article, they stock gluten free items, although at a higher price than other places: https://www.nytimes.com/2014/06/29/travel/gluten-free-dining-in-italy.html