HSA-qualified health insurance plans are available to individuals and families during the open enrollment period which lasts from November till mid-January, or if they qualify for a special enrollment period.
Self-employed individuals and 1099 contractors can sign up for a healthsharing plan called the HSA Secure, that also has an HSA component. This program is available year-round.
Once you have a qualifying plan, you can set up your HSA with any bank that offers them, and start making tax-deductible contributions.