It's pretty simple, through taxes. Most of the tax we would pay would be akin to the premiums we pay for private insurance... remember that we already pay medicaid and medicare taxes now.
The US pays more as a percentage of GDP for Medicaid/Medicare/Veterans healthcare than the UK spends on the entire NHS (which covers 100% of people).
This is often overlooked in the health care debate. If the US paid European prices for health care, the government could give everyone free healthcare without raising taxes at all.