You may still have access to your regular health insurance plan. Check with your employer to confirm if you can keep your existing plan.
If not, you may be eligible for COBRA or you may need to acquire health care insurance on your own. COBRA is the Consolidated Omnibus Budget Reconciliation Act and includes the opportunity for a temporary extension of health coverage (called continuation coverage) in certain instances. If you are eligible for continued health coverage, you will receive this information in your Benefits term notice. Continued coverage under COBRA is not guaranteed and is not free of charge.
Unemployment recipients, or even those who are without work and do not have access to unemployment (like 1099 contractors), may apply for health insurance via HealthCare.gov and receive a subsidy to offset their costs. Coverage can be as little as $1 per month with the subsidies.