The law can be determined but on a voluntary basis. This is one of the more "advanced" AnCap ideals and I'm not really qualified to explain it in detail. Essentially, you have to think of the law as a voluntary service that nearly everyone would choose to participate in, but would not be forced.
Let's say you steal something from me. I would go to a private court and file suit against you. If you ignored the suit, or simply were not able to satisfactorily dispute my charges, this particular court would find you guilty of theft. Depending on the prestige or credibility of the court, this would likely affect the willingness of others to trade or transact with you.
Essentially, the courts would be private reputation monitoring services, and in a society based entirely on trade, reputation is everything. I've linked this video a bunch of times in these topics and I'm not sure if everyone has ever watched it, but it sketches the outline of the idea.
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SmartMuffin - Because anything less would be uncivilized - http://img.imgcake.com/smartmuffin/barkleyjpgde.jpg
http://dudewheresmyfreedom.com/