Predominantly public: Government essentially takes over for insurance companies, contracting with doctors, hospitals and other providers and paying them directly. England does it this way, covering nearly all residents, and does not charge patients any co-pays or fees.
Mixed public and private: Combines private and public funds. France uses this system. Workers can get coverage through employers or through the government. In addition, the government regulates private complementary insurance that is also available. Patients pay a modest share of these costs, except in the lowest-income families, who pay nothing.
Other methods exist, too. For example, China has three major insurance types, covering people depending on whether they live in rural or urban areas and whether they are employed.
The common thread is that the government has made a significant commitment to being the main payer for health care.