Milano is known as the fashion city of Italy, but is much more than that.
The Piazza Duomo where is located the Duomo Cathedral, the Galleria Vittorio Emanuele II, the Palazzo Reale, Teatro alla Scala, La Rimanescenti store and all the magnifical buildings around it, represents the heart of historical Milano.
The Quadrilatero d'Oro, formed by Via Montenapoleone, Via Manzani, Via della Spiga and Via Venezia, is the fashion area where you can find the stylist stores (Zegna, Valentino, Armani, La Perla, Ferré, Vuitton, Cartier, YSL, Prada, etc). If the budget doesn't allow to shop here, just walk around to see what's fashionable.
Lets face it, Prada, Gucci, Giorgio Armani can be nice for window shopping but do you want the real deal beyond Via Monte Napoleone this is a short guide to streets worth visiting.
First up: In The Quartiere of Brera district, you can find art galleries and small clothes shops. Brera is the Artists Quarter with narrow streets with ancient buildings with lots of restaurants and cafés, tipical and artistic stores.
Second: Via Dante towards Castello Sforzesco can offer you some nice shops. It also hosts several Museums and is an interesting historical monument with a fantastic tower.
Third: Continue by foot or take the metro to the Navigli District. On weekends the sidewalks are packed with all sorts of funny things to buy, sunglasses, bijouteries and lots more. Naviglio is the Canals area, where is available an 1 hour boat tour through them (12 €, book first), with tipical and coloured houses, where people gather for happy hour (18:30 till 20:30, pay 1 drink and eat buffet), dinner or simply to have a drink.
Fourth: Go Viale Gorizia towards Piazza XXIV Maggio and up Corso Di Porta Ticnese. Plenty of cool shops, clothes, accessoaries etc on both sides of the street. Everything from vintage to brand names as Energy and Diesel. Stop for a coffeebreak at Basilica di San Lorenco, very nice. Closer to the Duomo shops will be bigger and here you can find more casual and sporty styles (Foot Locker, Camper etc).
Remember some days smaller shops open after 3 in the afternoon.