Getting a phone and a number is always one of your first concerns when going to live in a foreign country for a long time. To be honest, the easiest way to buy a brand new phone is to go to the mall, specifically Westfield Valley Fair (which can be reached by the bus #60 within 20 minutes if you don’t have a personal transportation). At this mall, there are different brands so you’ll have access to more available choices and can make quick comparison before decide on what to buy. I find this way more convenient rather than searching for a specific store and going there to find out more about what phone/contract you want to buy. Unless you know exactly what brand and what kind you’d like to acquire, Westfield is always a good choice. The most popular service providers around this area are T-Mobile, AT&T, Verizon.
Buying a phone is also easy. You don’t need any kind of paper just because you’re an international student. The buying process proceeds as usual: you buy your phone by cash or cards, then choose a contract plan. If you happen to have family or friends that you can share your line with, you can choose to use a package, which is way cheaper per month. However, if not, then you have to choose either a monthly plan or “pay as you go” plan. For my personal experience, a monthly plan is easier and more convenient because it usually gives you unlimited talk & text (but how much LTE data you get depends on the plan you choose, the more expensive the plan is, the more data you get).
In the case that you already have a phone from home, you can go online to your home carrier and have them unlock your phone for you. After that, the process of buying a sim card and choosing a plan remains the same as above.
In general, buying a new phone and getting a local phone number is an easy job. What matters is you should research first to see which carrier or which phone plan suits your lifestyle best in order to get the best deal.