The Duomo metro stop is larger underground than it appears. There are many, and I do mean many,…read moreentrances/exits to this station. Some has chair lifts to navigate steps but most entrances have many steps and some have long hallways leading under the Piazza del Duomo. Exiting you will end up in one corner, or another of Piazza del Duomo or near Via Torino if you walk a bit further along.
Once underground, you will see several automated ticket machines near the underground entrance turnstiles. Sometimes you will find a person there who wishes to 'help' you purchase your tickets. These folks are looking for a tip. If you don't need help, just say 'no grazie' and go about your business. The machines have language options to help. Once you have your ticket, scan at the turnstile and make your way down the escalators. There are maps throughout the underground to check you get on the correct train.
If you prefer to purchase your tickets from a person, head up the ramp (turnstiles will be on your left) and here you will find a small area with some shops and a ticket area. Many shops in subways throughout Milan will sell tickets. Just look for the "Biglietti" sign and have cash ready. The is often a line.
If you look around this area, you will see underground walkways leading off to the left. This long corridor is lined with cafe's and stores. Eventually, you will end up in the San Babila metro station where you can exit behind the Duomo shopping area. Lots of shops and some churches between San Babila and the Duomo.
Exiting at Piazza del Duomo you will find the Duomo, Duomo museum, Galleria Vittorio Emanuele the oldest indoor shopping arcade in Italy, Museo del Novecento, shopping and restaurants behind the Duomo, across the street from the Duomo you will find Piazza dei Mercanti a medieval square off the pedestrian zone that leads to Castello Sforzesco. You will find many stores, restaurants and theaters in the pedestrian zone.
Teatro alla Scala, a statue of Leonardo Di Vinci and Palazzo Marino are on the other side of Galleria Emanuele, just walk through. Panzerotti Luini, Milan street food, is on Via San Radegonda where you'll get a sweet or savory 'panzerotto' for just a few euro.
In the west corner the metro station exits onto Via Falcone, one block south of Via Torino which includes many clothing stores. Wander the streets off Via Torino into the Centro Storico section of Milan where you'll find cobble stone streets, archeological sights, many churches and ancient piazzas.
Good metro stop.