Montreal has an efficient public transit system consisting of buses, metro, and train. The cost, compared to other North American cities, is very reasonable.
You can find bus schedules at the STM site.
This metro map is interactive. If you click on the individual stations, you will learn about connections, points of interest, and much more.
Cost for the metro and bus depends on if you are paying cash, using tickets or buying a pass. There are tourist 1-day and 3-day passes as well.