The subway system is clean and fast compared to other North American cities of the same size. The buses are pretty convenient and they have nigh buses after midnight when the subway shuts down. It's worth mentioning that all public transportation operates entirely in French (no English translations), it's fine with me since I speak French but if you don't then be prepared to learn some basics (it'll help you with your entire existence there trust me).
If you don't feel like taking night buses after a night of bar hopping, there are always a bunch of cabs around (MOST of them speaks English).
As a full-time student at a university you are qualified for reduced-fare (48 dollars per month, unlimited rides) OPUS cards. If you are under 26. To get one you'll need some proof of your full-time student status (study permit, CAQ, or a Letter of Attestation from your school's registrar) and 14 dollars, head to the Berri-UQAM station where they sell the OPUS cards and get one.
Of course, you can always just rent a place within walking distance of your school and spare the monthly transport money all together (more $ for booze). Which isn't hard b.c rent in Montreal is dirt cheap even in downtown areas, split the cost by getting roommates.