Hi,
In most cases, a work permit is a requirement for a foreign national who wants to work in Canada. You will find below a link to the Canadian government website where you can apply. I suggest that you take a look at the International Experience Canada program, which may very well suit all of your needs.
http://www.cic.gc.ca/english/work/permit.asp
The easiest way to look for employment is online (I found my current job on the first website listed below, by the way):
http://www.workopolis.com/shared/en/home/index
http://www.monster.ca/
As far as accomodation is concerned, again the Internet is the best way to look, although many ads are written only in French by the landlords who are looking for tenants:
http://www.kijiji.ca/
http://www.lespac.com/montreal/immobilier-location-logements_b457df456dh0g17567i1j0k1wZ014Y2F0ZWdvcnlJZAR2.jsa
More luxurious apartments:
https://www.realtor.ca/Residential/index.aspx
Finally, I work for the largest private employer in Montreal and we hire a lot of recent graduates, but you should note, if you were not already aware, that Montreal job market applicants must carry a very specific set of skills: they must speak either French or English and often times both languages.
I hope this helps,
François