The night bus system is more or less a grid, with guaranteed connections at the bus stops next to two Metro stops, Atwater and Frontenac. All night buses have three digit numbers beginning with "3", and they start running after the day bus lines they replace stop running. This can vary from about quarter after midnight (on St-Laurent) to as late as 2AM (on Jean-Talon). They run at between half-hour and hourly intervals, and cost the same as day buses: $2.75, with unlimited transfers, including backtracking on the same or other routes, during a 90 minute interval.
For example, I managed one night last week to take the 51 bus out, walk to La Banquise, eat a late night meal, walk back to the 361, ride it up a few blocks, and just manage to catch the last 51 back home before I'd have had to wait for the 368 which replaces the 51, all on the same transfer. But I was lucky on my timing.
Probably the best bet for convention visitors is to pick up a 3 day transit pass, for $17, which is good on day and night buses and metro. There's also a 1 day pass ($9), and a 1 week pass ($20). The week pass isn't as useful for visitors because it is valid strictly by calendar week, Monday to Sunday.
You could drive instead, but parking is generally somewhat expensive and often hard to find because of permit-only spaces. On-street parking is often sold via kiosk, and can be a couple of bucks per hour. Fortunately, they do take credit cards.
For Bostonians, driver behavior is comfortingly familiar, with a French accent: you should be able to pull all the obnoxious crap you do back home in Montreal and fit in just fine, although you may find that someone more familiar with the street layout has beaten you to that "special" maneuver you were about to execute.
All bus stops include indications of the bus numbers which stop at that stop, the next Metro and commuter rail stop they stop at, and a bus stop code which you can key into (514) AUTOBUS, which will tell you when the next scheduled arrivals should be. (This is particularly handy when it's -30.) Most stops include printed schedule information, making a call redundant.
More information can be found at stm.info, along with system maps and journey planners. System maps and metro schematics can generally be obtained from metro station kiosks (although you will need to specify if you want a system map or they will hand you a pocket metro plan instead).
The city is fairly safe; there are no areas I can think of that a tourist would stumble into which might be dangerous, and even if you try hard it's difficult to find a place which is really dangerous. I've asked "Are there any no-go neighborhoods in this town?" of friends from Montreal and gotten a thoughtful look, and then a shake of the head. Not really, they seem to think. This obviously makes late-night transit a bit less risky. I still do watch it on empty streets after midnight.
Edit: I wanted to add this on the night bus system from http://cmeckhardt.livejournal.com/96487.html, because she mentions some things I forget. I do recommend reading her whole post, too.
"Furthermore, after the Metro ends (in the midnight to 1am range, check the lines you want and the day you're using them for details), there are night buses! Night buses! They don't duplicate the bus lines or the Metro lines exactly, and it pays to know the schedule of them if you can (the one I wanted to take came every 45 minutes), but if you go out late at night, you can get home! The buses go to both ends of the island and have two major hubs where the departure times of various routes are coordinated so you can transfer easily, Atwater and Frontenac. I strongly suspect that the night buses are why the platforms at Berri-UQAM are packed at midnight- because you can still be going places then! And you can still go home! (Though I freely admit your trip might suck if you don't know your bus schedule. I had a completely pessimal trip home one night where I walked most of the way from Mount Royal to Frontenac because I just missed a 97- and in the walking I just missed my night bus from Frontenac, so I had a 35-minute wait. But the weather was nice and I had a good book and I knew that might happen since I didn't have bus schedules, so I wasn't annoyed.)
"The thing that makes the night buses a little odd to navigate is that though they don't duplicate day bus lines exactly, they each have a day bus line they are associated with that they are considered to "replace", and night bus service for each bus line starts relative to when day bus service for that line ends. So whether you are taking the night bus or the day bus will be different at the same time depending on what bus you want. This is why for my pessimal trip home I wanted the 97 (a day bus) to the 364 (a night bus- the night buses are 3##). Again, if you can know your schedules it helps a lot."