Not a stupid question. Most people COBRA. COBRA is expensive but, like a group plan, automatically accepts you. Since the overwhelming vast majority of indie startups fail, COBRA usually lasts long enough to bridge you to your next job.
After about a year or so, if you're not certain you're going to end up with a full-time job, you need to look for real insurance. COBRA will last for almost another year, but when it ends it ends, and god help you if you're hit by a car or diagnosed with something nasty towards the end of your COBRA coverage (nobody will insure you).
Coverage from the majors costs roughly $400/mo. It gets much cheaper if you choose a high-deductable plan (you should), in which case you pay for all your health care out of pocket. A family of four can expect to pay over $10k/yr for low-deductable insurance, which is what virtually all companies offer.
Now, choose your own adventure:
Are you ~22 years old, male, with no dependents, with no long-term health issues and no prior history of hospitalization for illness? You can easily buy high-deductable insurance on the open market. There are several websites that will sell it to you.
Otherwise: you may be screwed. If you don't qualify for a group plan of some sort (which is how most Americans obtain health coverage), you may find that you are uninsurable. For instance, in the first year of Matasano, we tried to get private insurance and found that both my daughter and my wife were uninsurable. My daughter had been hospitalized for a freak seizure when she was 4. Erin has a functioning female reproductive system. NO COVERAGE. Not, "we won't cover the things we don't like". No, NO COVERAGE. Every insurer. The list of conditions with "deny coverage" attached to them, which most insurers publish, includes a wide variety of conditions experienced by tens of millions of people.
Good luck!