To find your way around Montréal, The D&P Guide is one place to start.
From the Airport:
There are a few ways to get from the airport to downtown Montréal.
1) Shuttle Bus:
A shuttle bus service, called L’Aérobus, runs between Montréal’s Trudeau International Airport and the Montréal Central Bus Station every 25 minutes. It also stops at major hotels. A one-way fare costs $14.00 while a 2-way fare costs $24.00. If you want to get to McGill University, you can take the shuttle bus to the Queen Elizabeth Hotel station (900, boul. René-Lévesque Ouest). The estimated time for this trip is about 40 minutes. The easiest way to get the McGill from the Queen Elizabeth Hotel is to walk north on Mansfield Street, then turn right on Sherbrooke. To go elsewhere in downtown, you may take the metro (subway); the Queen Elizabeth Hotel station connects to metro station Bonaventure (Orange). For more information about shuttle bus services, you may consult www.admtl.com and L’Aérobus.
2) Public Transportation:
Access from Montréal’s Trudeau International Airport to the city is also available through public transportation; it costs $2.75 (the cost of a cash fare) but it takes more time to get to downtown Montréal (estimated time is about 60 minutes). Find the STM bus station at the airport and take bus number 204 (direction downtown or centre ville). Get off after two stations (called Gare Dorval or Dorval Train Station) and from there, bus number 211 or 221 will take you to metro station Lionel-Groulx (Green).
The fastest but most expensive way to get from the airport to the city is to take a taxi, which costs a flat rate of $35.00 (+ a tip of about 10% to 15%) if you are going anywhere in the downtown area. The trip takes about 20-30 minutes.
For driving directions, consult the map.