For fares and schedules please go to the STM official website.
Using public transport is fairly easy in Montreal. Adult fares are 3$ one way and 5.50$ for a round trip ticket purchased at any metro station or via exact change on the bus. Tickets are valid for both bus and metro and can be used as a transfer ticket for up to 1.5 hours. The STM also offer three day pass options and unlimited 24 hour passes which are very useful so check out the website for exact fares.
There are many buses but the most important for students are the 80, the 55, and the 24. Both the 80 and 55 buses run north and south. You can catch the 80 bus at Place Des Arts metro station, where the UQUAM residences are located, and get off at Mont Royal or continue up to visit the Mile end and other neighborhoods. The 55 bus runs along Saint-Laurent Blvd on it’s way north all the way to the Jean-Talon Farmer’s Market. And on it’s way south it runs along Saint-Urbain street, stops almost in front of the UQAM Residence and continues down to the Old Port. The 24 bus runs along the longest street of Montreal called Sherbrooke street and will take students from the residences to campus in less then 10 minutes, which is useful on those very cold winter days.