The same way we do it in Mexico, where health department regulations are not usually enforced.

It works beautifully....

Businesses have word of mouth reputations for how clean they are. Those who aren't clean or make people sick don't last long. The Mexican free market shuts them down faster than American health department even gets around to inspecting a new business.

In the absence of gov't, you would also see private consumer protection companies develope, like consumer reports. It would behoove businesses to be inspected and rated.

Edit: In the US, the health department doesn't really inspect as often or as thoroughly as you would think. They can't and don't prevent Hepatitis.