There are actually three airports which feed into Milan, so it’s quite easy to get there from the rest of the mediterranean, mainland Europe and the rest of the world. The airports are Malpensa, Linate and Bergamo, and each is an effortless journey into the city centre by bus, so I’d pick your airport based on how cheap and convenient your flight is more than anything else.
Malpensa - The quickest option is the Malpensa Express, a train which shuttles between the city centre and the airport. You can either go to Piazza Cadorna or Central Station (which is further from the centre). The cost is €11 or €10 and the journey lasts 30 or 50 minutes respectively.
There is also a bus option from Terminal Two: one hour journey, €10 per ticket and goes to Central Station. Since the Malpensa Express only goes to Terminal One, so if you’re flying into Terminal Two and want to go to the city centre (not Central Station) then you should take the shuttle bus to Terminal One and board the Malpensa Express.
Linate - You can only get into town via bus or taxi, as there isn’t a connected train service here. Simply purchase a standard travel ticket (€1.50, valid for 90 minutes) and enjoy the 20 minute journey with time to spare.
The "Air Bus" goes straight to Central Station, which may benefit you more. It costs €5 and you can buy tickets on the bus.
Bergmano - It’s €5 for the bus to Central Station, or about €100 if you want to get a taxi.
Milano Centrale is an enormous train station, and one of the most important in Europe, handling around 120 million passengers per year. You can get here directly from all across Italy,and from all over Europe with a couple of connections.
The train station is a bit out of the historical centre of Milan, but the public transport system means you can travel across the city with ease.
As you’re probably aware by now if you’ve accepted a place at university in Milan, the city is absolutely massive. Sure, the strict city centre and tourist hotspots are fairly contained, but if you live there you’ll use so much more of the city than that - the public transport here makes that not just possible, but also pretty easy and cheap.
All three main transport methods in Milan - bus, metro and tram - are very well-developed, organized and well-maintained.
The metro has four lines, though the latest one (M5) is still under construction in parts so is a little less reliable. However, it’s also an ultra-modern gamechanger, so we’re looking forward to that being complete! Lines M1, M2 and M3 cover most of the city and as long as you’ve got an underground map and use the GiroMilano page to check for and works or delays, you’ll be set.
The buses and trams cover the rest of the city. There are simple maps at every station, and I’d recommend using the tram and metro over buses, as they’re more regular and more enjoyable modes of transport - they’re also more immune to traffic!
Ticket pricing is so simple in Milan it hurts me that more cities don’t do the same. A single, 90-minute journey ticket is €1.50. A pack of 10 costs €13.90. A day ticket is €4.50, and it’s €13.30 and €35 for a weekly or monthly ticket respectively.
You validate the ticket once you get on the bus/tram/metro, and you’re good to go! That’s all there is to it. Since it’s so easy and cheap, there’s no excuse for getting on without a ticket, and heavy fines will be given if you’re caught without one, no excuses.
The City Bike system in Milan - called BikeMi - is pretty good. There are 4,500 bikes, of which 1,000 are electric. The annual subscription costs €36 and entitles you to 30 minutes free riding per session. Thereafter you have to pay around €1-2 per hour, so the smart thing to do is dock the bike after nearly 30 minutes and take out a new one if you’ve still got a fair way to go.