Costs:
The cost is about 25% less than in Seattle although Seattle is one of the most expensive places to live, so take that with a grain of salt
You do pay for transportation by a subway a bus or a tram for about 2.20 euros for 90 min but you can also buy tickets in bulk if you know you will be using public transportation quit often for 19.50 for 10 tickets- the deal is cheaper than individual ones.
This is very cheap compared to transportation in the U.S. like a car.
A euro is about 1.06 dollars so many things will feel more expensive because of the exchange rate.
There are luxury brands all around, this can pressure you into buying them while you walk around the city. So just be aware of this.
Tips:
Bring walking shoes! Walking is the most common ways to move around the city because the city is quite small. If you don't bring good walking shoes your feet will hurt!
Pick pockets are very common in Italy especially in crowded areas like common shopping areas, subway stations, and train stations. Tourists are number one target simple things not leaving things in your pockets, double check your stuff every so often, and walk with a confident persona.
Bringing at least a little cash with you is a good idea, many places are cash only rather than card. even though cash is easier to pick pocket you wouldn't want to be caught with no way of paying.
Conclusion
The style of life is quit different from the U.S. but the adjustment is relatively doable! Like in any place you go stay safe in places you see and learn may not be the safest, and don't be shy to act like a tourist. You are going to be living there for a whole semester and you might feel inclined to act as someone who truly lives there but your not, be your self. Milan Italy is a beautiful place, look around, do things, ask questions, interact with the area round you and have fun learning new things and experiences!