My very first huntard question

[silverthorne]

Which is:

I understand that to learn certain pet skills, you have to tame a pet with that skill.

What I'd like clarification on:

Does taming the pet automatically teach you any unique skills it has?
Or does it make that skill available to buy at a pet trainer?
Or is there something you have to do with the pet itself to acquire the skill?

Pretty much, the instructions I'm finding say 'tame new pet; learn new skill; teach new skill to older pet (if applicable)'. But the 'how' part of the hunter learning the new skill seems to be missing...