How can I find an apartment in Montreal?

You can reserve a temporary residence before coming here and if you spend some time you'll find a good apartment very soon. In order to start, just join http://groups.yahoo.com/group/iraniansinmontreal and take a look at "Links > Montreal > Apartments". I recommend the following links:
http://classifieds.canada.com/montreal/
http://www.mcgill.ca/classified
http://english.montrealplus.ca/portal/index.jsp
http://hojo.csu.qc.ca/dev/
http://www.mcgill.ca/offcampus/
http://www.laberge.qc.ca/default.asp?Lg=en

Off-Campus housing (from Concordia University Website)

If most of your classes are downtown, or you’re an older student, or you simply prefer choosing your own type of living accommodations, then the off-campus option may be best for you. The Concordia Student Union (CSU) maintains an off-campus housing bank.
While Montreal is still surprisingly affordable for a major North American city, rents have been increasing steadily and apartments have become harder to find than in the past.
In general, apartments can be found close to both Concordia campuses (NDG and around Guy St. downtown, or in areas nearby). Here is a short description of some popular student areas:
NDG and environs: This is an affordable, fairly clean and quiet residential area, with a good sense of community. It’s great for students at Loyola, not as convenient for those studying downtown. Public transportation is available, however. Note that there’s not much of a nightlife here.
Downtown: Apartments near Guy St. are usually in high-rise type buildings, and a couple minutes’ walk to campus. Further east, there’s the ‘McGill ghetto,’ where walk-ups are available. Downtown apartments tend to be expensive, and their level of cleanliness varies greatly. However, you have access to great nightlife and transportation.
Plateau Mont-Royal and Mile End: The Plateau is many students’ preferred location because of its access to nightlife, shopping and more attractive living spaces. However, gentrification has meant that prices have increased dramatically, yet apartments are harder than ever to find. The spillover has gone further north, to Mile End.
Little Burgundy/St. Henri/Verdun: These areas still have cheap housing available, and they’re near metro lines.

Montreal peculiarities

1- Find out if major appliances, such as refrigerator and stove, are included, or if you will have to find your own.
2- Apartment sizes come in the following: a 1 1/2 is a large room with kitchenette and bathroom; a 2 1/2 is larger, or has a double room or is L-shaped; a 3 1/2 has a separate bedroom, living room, kitchen and bathroom; a 4 1/2 has two bedrooms, a living room, kitchen and bathroom; a 5 1/2 usually has three bedrooms, and so on.
3- Find out whether heating is included. If not, plan for winter costs.