As such Milan is not considered a tourist hotspot. But it is however, the second most important city in Italy in terms of flights in and out. Its international airport Milan Malpensa connects several international destinations with Italy. This however, makes it all the more difficult to find cheap flights to Milan considering that people are constantly scrambling for tickets.
Milan has two primary airports and this should help you narrow down cheap flights to Milan. Besides the large airport of Malpensa, Milan has a smaller airport at Linate. Milan Linate however services most of the low budget airlines. The thing with Milan Linate airport is that you may not be able to fly into it directly from an international destination. But what you can do is fly to a destination within Europe and then look for flights into Linate. This airport is located in central Milan and therefore is a cheaper bet in terms of travelling into the city. Travelling by taxi from Malpensa is prohibitively expensive and a deal you should avoid if you have the means.
Irrespective of the airports you fly into, getting cheap tickets to Italy can be quite task. Alitalia is the national carrier and treats Malpensa as a hub. However, the airline has been financial troubled waters for a while now and tickets on it can be expensive. While Malpensa has most of the airlines flying into the airport, Linate has several budget airlines that fly into it and therefore can work out cheaper. The most important is to book your tickets well in advance. Ticket prices are higher between April and in early October. Italy as such does not have an off season, but you would definitely get good rates if you are travelling outside of these dates.
Another good way to get cheaper tickets is to fly into Linate from different European city. You could also choose to do this at Orio al Serio, which is now slowly being considered a third airport. Most low budget airlines fly into them. If you get yourself a good deal for a ticket into London or Frankfurt and then into Linate, the deal is bound to be a lot cheaper.