Flights to Milan arrive into either Linate, or Malpensa international airports, and trains, taxis and buses are all available to get you into the city centre.
Once there, it makes sense to buy a Welcome Card, which vary in price depending on how long you want one for, but allow you to use the excellent public transport free of charge, and also offer reduced price admission to many of the museums and galleries in the city, as well as store discounts.
The Lombardy area surrounding the city lends itself well to a driving holiday, and it is possible to hire a car in advance of travel in order to explore the area close to Milan.