Initially there was a hodge podge of coverage. You had some private insurance, some employer co-pay insurance (much like in the US), and then the poor would be admitted to hospital on a charity basis, essentially. The way it evolved was basically like this: first, in Saskatchewan, a pilot program was started giving every citizen of SK free hospital coverage only. Then, a second program in a smaller town (can't remember which one off the top of my head) provided all the citizens in that town with complete, universal health insurance. When other provincial governments saw that this was functioning well and efficiently, a national commission was established with the view of expanding it throughout Canada. In 1958, every Canadian had free hospital services and 10 years later, the Medical Care Act was passed. This was eventually modernized into the act we have to day, The Canada Health Act, which establishes an agreement between the provinces and the federal government, outlining the five criteria which the provincial healthcare systems had to meet to qualify for a full federal cash contribution.
I will give you some statistics, as well so that you can see that this private healthcare by no means guarantees you more service or better service.
The OECD published a study in 2003, outlining health expenditures. The US health spending is 15% of total GDP (compared to Canada 9.9%, UK 7.7%, France 10.1%, Germany 11.1%, Japan 7.9%, Denmark 9%, etc). However, when you look at the # of acute beds per 1000, the US has less than all those countries. It has 2.8 acute beds/1000, compare to Canada 3.2, Germany 6.6, France 3.8, UK 3.7, Japan 8.5, Denmark 3.4. The US does have more MRIs per million than the UK, Canada, France and Germany, but lags behind Denmark (9.1 vs. 8.6) and REALLY lags behind Japan (8.6 v. 35.3).
The same study looked at other comparisons. The US has a lower life expectancy at birth than Canada (both men and women), a higher infant mortality rate, comparable cancer rates, considerably higher rates of cardiovascular deaths, higher rates of diabetes, obesity and smoking. I won't even compare to European countries because there the disparity is enormous. Plus, Canada and the US have more similar societies than the Europeans.
So that's just a quick overview for you.