There are shuttles from the airports to train stations in the city. Despite the fact that service stops around midnight, the subway and bus are probably the easiest way to see the city. Allow yourself extra time for connections, as the trains often run late - and the Stazione Centrale, the main train station, can be a bit daunting. You can buy tickets at newsstands and ticket agencies, and in a few of the stations, but not on the trains. The Stazione Centrale is the departure point for virtually all the major cities in Italy.
Buses leave from here, too.
Cabs are plentiful, but really expensive. Obvious tourists are targeted by pickpockets and con artists. Even crooked train conductors will take advantage - if you let them. Milan is a big city, so use common sense. Be careful of your stuff and yourself, and don't walk alone at night.