Independent Contractor.

Hey guys. I've seen a bunch of posts with questions similar to this, but would like to post anyway with my example and question.

If I where to have an American company willing to hire me (a Canadian living in Canada) to work from home as an independent contractor, not an employee of the company, what would I have to do? I would be paid in USD, and would never need to leave my home office. Would I need to file taxes in the US? What would I have to do here in Canada? Any info would be helpful!

From my understanding, I would invoice the company, and they will send a cheque. I would not need to pay taxes in the US, however I would pay taxes in Canada as self employed. Also looking at Canadian pension plan, I would probably have to pay into that as well. Am I making any sense?