As an independent contractor in Canada, my client pays me, just like he would any other bill. There is no payroll withholdings for them, on my behalf, and it was the same when I was a sole proprietor, before I incorporated. I charge GST (sales tax) because I sell more than $30,000/year worth of services.
It's the same as if you went into a car repair shop. You (the client) just pays the bill, you don't do any sort of payroll mumbo-jumbo for the car repair shop, even if you are claiming it as a business write-off.
I hope that helps a little.