A free society necessarily has private courts and protection agencies (because there is no state, and because criminals are expected to always be with us).
How could this work?
First, Justice in a free society—it's about harm, not crossing arbitrary lines. It first belongs to the victim; but that doesn't mean everyone has to sit on their porch with a shotgun looking for burgars; the services of protection and arbitration can be bought and sold on the market, likely through a subscription model.
Some excellent articles on implementation:
Murphy's Books/PrivateLaw and Books/LawWithoutTheState (video).
Hasnas's Books/TheMythOfTheRuleOfLaw.
ClearSay's Law Without Government.