In a nutshell, each pet has its own skills which work just like a player's skills do. As in the pet gains in skills by using those skills. You don't have to choose anything, the pet has certain skills that it will get better at through combat.

Like, most pets have wrestling, tactics, anatomy and resisting spells. Magic using pets have also magery, eval and meditation. Some pets also have poisoning, and the cu sidhe has healing.

Each pet you tame has its own skills and they don't affect other pets in any way like apparently in WoW, so no worries about having to tame certain pets to use their skills.