The way pet skills work in WoW is that the hunter has to learn the skills first and then he/she teaches those skills to any pet capable of learning them. Some skills can be learned, bought, from a pet trainer. But others, such as bite, have to be learned from other beasts by taming them and fighting along side them until you have learned that skill.
Here’s a link to Petopia’s article explaining how the system works (http://petopia.brashendeavors.net/html/articles/skills_main.shtml). Also take a look at their list of pet skills to learn which beasts can teach you the different ranks of the different pet skills. And while you are there you should also take a look at the various types of pets. The site lists all the pets and all their different colors.
If you would like even more information, read the sticky at the top of this forum. Page one talks about the hunter and page two talks about the pet.
Good hunting.