So, just the basics so far, once you begin pet training you are given a % Finished bar. Monsters give anywhere from Slightly (.02-.05) up to Greatly (.70)% randomly when you take damage or give it.
Summons can be used, and your own pets can be used, but they seem to give the .02 gains. Which would take a long time, but would be scriptable for sure.
Still not sure exactly what determines how much you gain from monsters, but it has to be tied into fame/hp/barding difficulty/something.
I'm still only messing with 2 slot pets.