Since it's a bit unclear how exactly you teach your pet abilities other than Growl, here's a quick guide on how to do so.
https://dl.dropboxusercontent.com/u/223 ... tiary.html
This page lists all tameable pets, their stats, and what abilities they can learn. On each individual creature, it lists what abilities that creature knows by default when you tame it. That's what you're looking for.
For example, if you look at Great Wetlands Crocolisk, it is listed as having "Bite 4", aka Rank 4 of Bite. That means when you tame that creature, it will know Rank 4 Bite right off the bat.
Now, in order to teach that ability to other pets, you'll first need to "learn" the ability yourself. Basically you need to take that new pet you tamed, and just have it use its ability over and over again until you see "You have learned (ability Rank X)" pop up in your chat window.
This can sometimes take just 1 mob, or 7-8, depending on the ability. Bite has a 10 second CD, so I had to kill a bunch of mobs with my pet before I learned it. Claw, however, has no cooldown, and I learned it halfway through the first mob my pet killed.
Now, the ability will show up under the Beast Training menu, and thus, you can teach that ability to other pets that are capable of learning it. Remember that higher ranks of abilities have certain level requirements.