Milano is served by a very good public transportation managed by ATM. There are three underground lines connecting the main places of the city and a good amount of buses and trams, which will get you almost anywhere you want.

 
The price for one ticket in the city area is € 1.5 and it is valid for only one trip in the undergroung or 90 min's on buses and trams. There are also a daily ticket and a "carnet" which is ten tickets for a lower price.
 
 

METRO CITY MAP

CENTRE MAP

If you have to live in Milano for more time, maybe you should be interested in a monthly or even yearly card. They are pretty cheap for students.
 
The monthly ticket costs € 17 every month, plus € 10 the first time for the card and a picture (fototessera). The cost of a yearly card is about € 160 and it is valid 12 months.
To get your ATM card, you have to go to one of these offices inside the underground: - Duomo (MM1 and MM3) - Loreto (MM1 and MM2) - Cadorna (MM1 and MM2) - Centrale (MM2 and MM3) - Garibaldi (MM2).
 
Have a look on ATM web site to find buses and tram timetable, or to find the right path to reach a destination.