Buck is introduced to primitive law when he first witnesses a dog fight. He sees how rank and order fall within a pack of dogs, and it is this first experience that inspires Buck to eventually become the lead dog.
Buck learns through watching and observing the other dogs just how he will be expected to behave within the society of canines, and as a result, Buck gets involved in several fights of his own with other dogs as the chapters unfold. In addition to his understanding of dogs, he learns later that man is to be obeyed at all times, a lesson he is taught by the man in the red shirt who beats him severely.
I find your question very interesting because of your use of the term "primitive law." That certainly is a fancy way of referring to the natural law of creatures on earth, but a wonderful way to ask the question. Why? Because the first chapter is called "Into the Primitive," and rightly so. In short, Buck's introduction to primitive law comes when he observes a pack of dogs fighting early on in the novel.
These men wanted dogs, and the dogs they wanted were heavy dogs, with strong muscles with witch to toil, and furry coats to protect them from the frost.
Buck only truly understands this after the dog fight is witnessed. Before this, Buck thinks as any domesticated dog might think. Unfortunately for Buck, he is stolen away from his domesticated life and forced to brave the harsh life of the Yukon. The dogs fight with rank in mind. The lead dog is very evident, and it is this position that Buck wants to obtain within his eventual pack. By watching this pack of dogs, Buck learns exactly what is expected of him. Canines have their own particular "society" within the pack. Of course, in order to obtain the position of lead dog, Buck is forced to begin fights later on in the novel.
In conclusion, there is also an important part of primitive law that is prominent in canine society: obedience to man. How does Buck learn this? From the man in the red shirt who beats Buck quite badly as a result of his lack of obedience. Even this submission is necessary for survival and part of primitive law.