That depends on the program. Two approaches have been proposed in California in the past. One would keep insurance companies as they are, and the government would pay them, in the same way insurers work with many Medicare and Medicaid patients now.
The other approach would eliminate insurers. The government, rather than insurance companies, would contract with medical providers and pay them directly. Supporters of this plan argue that insurers, with their well-paid executives and other high overhead, are the reason health care is so expensive, and this is a way to both reduce costs and streamline the care and payment systems.
Insurers disagree. They say consumers deserve choices about health care. And Kaiser Permanente has said eliminating insurance companies would disrupt its entire business because it is both an insurer and a medical provider.