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.
The easiest way to look for employment is online (I found my current job on the first website listed below, by the way):
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:
More luxurious apartments:
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,