I'd like to explore British Columbia, for maybe a few months. I see this being expensive and difficult without a visa, but I don't mind working, even in a stipend position that only covers living expenses.
What such programs, if any, are out there?
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There is NAFTA, which if you are eligible makes it really easy to work in Canada as a US citizen. But the provisions in NAFTA don't apply to most people. "NAFTA applies to four specific categories of business people: business visitors, professionals, intra-company transferees, and traders and investors." "Professionals" is defined pretty narrowly; the majority of people would not fit into those four categories. You can't just go up and work on a farm or in a restaurant or something. (Computer programming would be eligible for example).
If you're not covered by NAFTA, you'll need a work permit. Exceptions are made for those working for foreign companies and such as well, such as airline workers; it would be silly for them to need a work visa every time they were on a Canada-bound flight. See http://www.cic.gc.ca/english/work/apply-who-nopermit.asp for more details on that.
There's a Working Temporarily in Canada page that leads to some good info, such as who can apply. In general, you need to have a company willing to hire you to sponsor you through this process. You can go as a visitor and find work, but normally would have to leave the country and re-enter on the work visa before starting work. The eligibility page says that you can't apply from within Canada unless you are switching jobs or are a student in Canada, but again I think you should be able to leave and re-enter.
In order to work in British Columbia as a Temporary Foreign Worker (TFW), an individual will normally need to get an Employer-Specific Work Permit. This usually involves obtaining a qualifying Canadian job offer from an authorized employer in British Columbia (or elsewhere in Canada) and may require that the Canadian employer receive a positive Labor Market Impact Assessment (LMIA). You mightfind it helpful to visit Canada’s Job Bank to search for open positions in British Columbia.