Montreal has a fantastic public transit system (STM) that can get you nearly anywhere on the island.
To use public transportation, you can buy the rechargeable OPUS card. You can buy a regular OPUS card at any metro station and it can be used for the metro and buses. There is a reduced fare for students, for which you will need a personalized OPUS card that you can apply for through the Concordia system. You can find more information .
Once you have an OPUS card you can recharge it at a machine at a metro station or on the "Chrono" app.
Metro
The metro system (AKA, the subway), consists of 4 lines named by color (orange line, green line, yellow line, blue line), which connect at designated stations throughout the system (see image below). Metro directions are named by the last stop on each line, and will be posted above the passage for each stop. For example, to get from station Bonaventure to station Vendôme, you would get on the orange line, in the direction of Côte-Vertu. If you plan on going somewhere new, I recommend looking up the closest station to you via Google maps or Montreal's public transportation app, "Transit". You can get nearly anywhere on the island via metro, except to the West Island, which can only be accessed by train or by bus.
Bus
Montreal also has an extensive bus system. Each bus is numbered, and will either run East-West, or North-South. Make sure you get on the bus going in the right direction, so you don't get lost. Each bus stop will be marked with the buses that make a stop at that location, as well as the last stop on the bus to mark which direction the bus is running. Some buses, like the 105 which you will need to take to come to campus if you get off at Vendôme metro station, run approximately every 10 minutes. Others that take longer commutes, come less frequently. Buses are generally pretty on schedule. To get (usually) real-time wait times of the buses, you can download Montreal's public transportation apps "Transit" or "Chrono", which will show you all the buses running nearby, and their arrival times.
You will need to notify the bus driver of your stop by pushing a button or pulling a cord on the bus once the bus departs from the stop prior to yours. If there is no one getting on at your stop, and you haven't pushed the button, the bus driver will assume they don't need to stop and will continue to the next stop. This isn't too bad on local busses, like the 105, but can get you quite lost on longer commute busses.