The best driving tip for Montreal is simply not to drive. The public transportation system will get you anywhere you want to go.
If you do insist on getting behind the wheel, keep in mind that all road signs are in French. If you don't know French, getting around can be a challenge. Learn these basic conventions before taking out your car: Nord (North), Este (East), Sud (South), Ouest (West), Sortie (Exit), Pont (Bridge).
Montreal uses metric units. The freeway speed limit is 100km/hr. In the city it generally ranges from 40 to 60km/hr.
There is no right turn on red in Montreal, and left hand turns are also generally forbidden. Most of the streets downtown are one-way, so keep an eye out for that. The roads are well marked, though, so as long as you’re vigilant this shouldn’t be much of an issue. Also watch out for special lanes dedicated to taxis and buses. Seatbelts are also mandatory, as are helmets for motorcyclists.
Parking can be a little pricy, starting around $3/hour or $25/day. Finding street parking can be difficult, especially in the inner city. Be aware of parking restrictions in the winter, as ignoring the rules of snow removal can result in a tow and a fine.
All that being said, Montreal is a fairly drivable city. Traffic is better than most large cities. You don’t have to worry too much about crazy drivers either.