Wireless internet access is widely available in Milanese hotels, cafes, shops, museums and restaurants, usually free of charge (although some of the very top end hotels still charge upwards of €10 per day for access). There's also free city-wide access at info.openwifimilano.it although it isn't always reliable.
If you don’t have your own computer, a few of the higher-end hotels will let you have use of a computer or iPad. Otherwise, there are just a handful of internet cafes charging €2 to €6 per hour. Some cafes will request ID in order to use their facilities.