Some governments do so by starving the health system of funds, making public care so inadequate the public reluctantly turns to private health care for services.
This is what the Alberta Conservatives have done with programs over the years. Blowing up hospitals is one way to short services.
As a PS, this is an example of the system The Conservatives are putting us into!
Stelmach recently said "There is no hidden agenda" meaning there is sufficient publicity around their intent to privatize health care that it is no longer a secret.