www.stm.info
It should be noted that the former STCUM is now known as the STM, for Société de Transport de Montreal. This is because the island of Montreal recently merged under the "one island, one city" proposition. As such, it is no longer merely an urban community.
It should also be noted that the STM does, in fact, fucking rock. The system is ridiculously simple and efficient. Essentially, at every metro station, a particular track is identified by the stop where it ends up. From there, you can easily figure out how to get to where you're going by the system maps provided at every station. Any location downtown is accessible within a few minutes.
The STM is affiliated with the AMT, or Agence Métropolitaine de Transport. These guys are essentially responsible for running the commuter trains. Why the two companies never merged is beyond me. Nonetheless, they achieve a remarkable synchronicity. The same pass allows you to take the train from nearly anywhere in the suburbs straight downtown without ever being delayed by traffic (obviously) or bad weather. This is a Good Thing, since Montreal is famous for its debilitating weather. As an example, most elementary and high schools expect you to show up if there's been two feet of snowfall overnight. We also have an excellent (albeit extremely costly) snow-removal system, but that's another topic for another node. These trains also take you a good distance off-island going in the opposite direction, going as far as Rigaud. To take them beyond a certain proximity to downtown, however, requires a more expensive, extra-"zone" pass.
The pass in question is now 25$ for students, with a new extended deal for university students for a little more, and about $45 for adults and non-students. They recently began advertising on the passes; why they didn't think of this before is incomprehensible. They probably make a killing, and I'm just happy for a deviation from the neon-coloured generic monthly-themed symbols. More power to them. Anyway, to be considered a student in the STM's eyes, you need to have a photo ID card made once a year. The photo is always as horrible as it could possibly be; don't try to avoid it.
The public busses, if a bit less reliable, are extremely versatile. Typically, they can take you to within a few blocks of any given point on the island. There are busses dedicated to night service as well as rush-hour-only express busses.
Also thanks to the STM/ATM cooperation, most major bus terminuses, metro and train stations coincide geographically. This makes switching routes and systems stupidly easy.
Some claim that STM bus drivers are generally bitter. I wouldn't say it's a rule. Some are deliberately mean, some are indifferent, some are damned kind. All three categories take a fairly equal proportion. What it comes down to, though, is this: if you're on time, you have a valid pass (and student card, if applicable), nobody's going to go out of their way to be unkind.
Finally, the STM maintains a fantastic website. It contains a complete system map, one exclusively for trains and another for every system on the island. Available as a 2-meg PDF, it's insanely useful, since every single street (and street name, for that matter) is mapped out, along with bus routes, terminuses, metro and train stations. It makes just finding a street address a simple task, since you simply perform a search for the name of the street, and it zooms directly to it with the name highlighted.
It also has full listings of the exact time at which a bus will pass a given stop, and a host of other features. It can be sought at www.stm.info.
A last convenience offered by the STM is phone numbers printed on every stop for every bus. Simply dial the number, and you're told when the next three busses will pass. the call is free (excluding cell phone minute charges).