Wiki - Pet Training
Training a pet in UO can be frustrating for the inexperienced. A full explanation of how the system works can be seen on uo.com's Wiki here.
The Animal Lore and Taming required to control a pet increases by 10 per additional slot trained onto it, to a maximum of 118.
Some of the stat limits have been altered on Legends of Sosaria to allow for slightly stronger pets.
Pets that are training will gain experience based off their barding difficulty versus that of their opponent. It should be mentioned that barding difficulty is a calculated number, not set, and not all monsters of the same type are created equal. This means that you may not gain from every monster of a particular type. The best advice we can give you is to move to a slightly tougher enemy should your pet be resisting getting gains.