This is exactly right. A free market has no government regulating it. It is self regulating.
If prices go too high, people stop buying, and buy something else, or a cheaper alternative from a competitor.
If prices go too low, the businesses are not making a good profit anymore and could wind up going out of business as a result.
A business wants the highest price it can get for it's products.
A buyer wants the lowest price he can get for the products.
The two negotiate (often using a middleman marketeer such as a broker or warehouse (store). Somewhere in the middle they agree on the price.
This is called 'price discovery' and is an inherent component of any free market.
The free market is immortal. You can't kill it, no matter how oppressive a government. It will always exist, even if it's driven into a black market. See your local drug dealer for details. Even he has to compete against other drug dealers and there are plenty of buyers willing to pay that price.