The company managing all public transports in Milan is called ATM (Azienda Trasporti Municipalizzati).
There are 5 metro lines with 136 stops and more than 110 km of rails named M1 (red) M2 (green), M3 (yellow) M4 (blue) and M5 (purple), 17 tram lines, 147 bus lines, 4 trolleybus lines, 19 suburban train lines, moving almost a billion people a year… so you most likely will be always really close to a stop.
And this is how an underground station sign looks like:

You will realize that moving around is quite easy and cheap. On the other hand fines if cought without a ticket are really hight.
First and most important: ATM is NOT selling tickets on board! You must get one from vending machines, tobacconists or newsagents before boarding.
Easy way: just use your contactless Credit Card as a ticket and ATM will automatically charge you the cheapest fare according to how you used the service (for example: 2 rides in 8 hours = 2 single ride tickets, but if you take 4 it within 24 hr it will turn into a 24 hr pass automatically so you will save 1 euro). It may charge a few euros upfront as a deposit to be sure the card is working.
Most common tickets are:
- single ride: the price is 2 € , you can use any line for 90 minutes
- 24 hr pass: the price is 7 €
- 72 hr pass: the price is 12 €
Keep your ticket\credit card handy when getting off the undeground train as you’ll be asked to swipe\tap it again.
Anyone under 14 years old travels for free but bring an ID as a proof!
You can download a complete map of the underground and suburban rail system here.
You can also use ATM journey planner here, but Google Maps is 100% integrated and works well.
During the night, only a few lines are active. Buses covering the same route as M1, M2 and M3 are active all night long, and also trolleybus 90\91. Have a look here for more details.