There are several options to eat cheap in Milan, depending on your taste and on your budget:

- a Pizza in one of the thousands of pizzerias with a beer will cost you around 15 euros including a coffee at the end, 20-25 if you also take a dessert or a starter.

- a panzerotto at the famous Luini bakery will cost you a couple of euros, with 2 of them and a coke you will be ok for lunch

- a mixed salad or a piadina in any of the  bars in the centre, with a drink, will cost you around 10  euros, it's the typical lunch break of those who work in the offices around the Duomo square

- a panino in any of these bars will cost you around 4€, a panino is usually a sandwich with ham and/or cheese and/or vegetables which is generally heated in order to taste better, if you never tried it it might make sense to do it once. The best place to have one (slightly more expensive but so much better than the average) is "Al panino Giusto", there are several locations around Milano, check on 

- another interesting chain is pastarito, which is a chain specialised in pasta and pizza at reasonable price. A large plate of very good pasta with a good sauce + a drink will set you off around 12 euros.

- finally, if you are lucky, particularly in less central areas you can find Trattorias with "menu fisso" which will offer you a set menu for lunch at around 10 euros. You can recognize them because if you go there between 12 and 12.30 they will be full of blue collar workers who have their lunch there.