Visit Italy during its off-season, which happens every summer and winter. During the spring and fall, the country is full of tourists: That's when airfare and hotel prices sky-rocket. When fewer visitors are making the trip to Italy -- during the off-season -- the price of airfare drops considerably.
Research flights on different airlines. Use a travel website that shows multiple flight results for each search. You'll quickly see which airlines offer the best rates.
Plan to be flexible. Sometimes rates on are lower the day before, or the day after, your chosen date of departure. If you can allow for date flexibility in your travel plans, it is wise to do so.