Milan is located in Italy, so we expected to see familiar things like rubbish on the streets, mad drivers and even madder motorcyclists. We got it right, with one exception - the city center (remember Milan still holds the title of the fashion capital of Europe), with its fashionable boutiques like Prada, Gucci etc.  
Prices are way too high, for example an ugly looking Louis Vuitton handbag is 2 000 euro. Big sales start in January and reductions (Italian scónto) could  reach up to 50-70% or even entire 80%! So it might help a little bit.
A cup of cappuccino can cost as much as 4-5 euro in the city center but if you go a few stops further by tram you could get the same good cappuccino for just 1.50 euro!
In the evenings the so called “happy hour” is very popular - you just buy 1 cocktail (5-8 euro), and all cold and hot snacks are free of charge, you can eat as much as you possible can! 
The famous Duomo cathedral (1386-1813, it took almost 430 years to complete!) is actually very beautiful - enormous in size (it's the third largest church in the world) and of bright tones, a good contrast with the remaining parts of the city with its rather gloomy tones. 
I especially recommend a visit to the roof (on foot - 5 euro, on the elevator - 8 euro). It's absolutely stunning, lots of intricate figures of medieval masters will leave an unforgettable impression.

The Last Supper, Leonardo da Vinci's masterpiece is an absolute must-see in Milan - the fresco is actually huge (I have seen it many times on telly or in books but never realized it could be as big as this) and takes up a refectory wall in a Dominican monastery. Entrance by reservation only (phone or go online), but we had just a few days in Milan, so we talked to a staff member and he persuaded the guide of a Japanese group to take us "onboard"! Lucky us!
For art lovers, it's very interesting to visit Pinacoteca di Brera - the largest in Milan and one of the best in Northern Italy. There it is possible to see the  works of such masters as Mantegna (“Dead Christ”), Rafael and our favorite, Caravaggio's “Saint Sebastian” (a saint, who on emperor Diocletian's orders, was pierced by arrows, but miraculously survived).

In Milan all forms of transport are represented: the metro (completely tasteless interior), old wooden trams (plastic seats are too cold to sit on them), trolley bus (Italian "filobus") and buses (using gas instead of petrol). They all use the same ticket and it's pretty cheap (for instance, a 24-hour ticket costs 3 euro).
Getting around only in English is quite problematic, so  I  would recommend using some “magical” words like buon giorno (Hello), grazie (thank you), arrivederci (goodbye) and mi scusi (excuse me). 
Milan's Duomo
On the roof
La Scala and tram
Just like in Venice
"Automatized" lawn
Reserved for Irish policemen only!