To start: For some excellent tips on someone starting conversion, see this question and its answers:
First steps for someone considering conversion
As DoubleAA noted in his comment, studying conversion is something that is usually, but not always, done at a personal level. That being said, there are many classes one can go to about Judaism that are given for Jew and Gentile alike.
I recommend that you get in touch with a Rabbi in the neighborhood you plan to move to. Ask him about what classes he offers, and whether you can join. Be up front about being non-Jewish, but really, that should not deter any rabbi from teaching you. Some may not offer classes on your level of learning, but they should be able to refer you to a rabbi that does. Certainly, before studying specifically for conversion, you should attend a few classes and speak to a rabbi face to face about it.
And now, on to the question!
As far as organizations go, Chabad is a world-wide organization that has rabbis everywhere. More importantly, they put great importance into outreach, and are accepting of anybody, Jew or non-Jew.
For a list of all their Canadian centers, you can check the Chabad.org website. (Toronto, Calgary, Halifax, Kingston, Ottawa, Vancouver, Winnipeg, etc., etc., etc.)
Another organization that specializes in outreach is Aish. They are a world-wide organization as well, although they appear to only have one center in Canada: Toronto.
Both of these organizations offer classes for beginners to Judaism, so they should be exactly what you want.
If you can't find a rabbi that is able to work with you, or you want to skip straight to those that work on this all the time, get in touch with one of these organizations.
(Incidentally, much of the outreach in Montreal is bilingual, in my experience. I don't know if that matters, since you didn't specify where in Canada you are going.)