In Draenor, the tradition of adding a pet trainer to each region was continued. There is a total of six trainers spread throughout the map which you can travel to and fight against.
is my special recommendation to visit every day, since the fight is quick, super easy and you can bring not just one but even two level pets! And even better, they can be level one. There are not many opportunities to jumpstart two squishy level 1 pets at the same time with a good deal of experience gained at it. Definitely worth trying out! And if you own the Garrison portal building, you can even open one that leads almost directly to Ashlei.
The main strategy for every fight is optimized to bring a leveling pet along, allowing you to level up pets very fast. Most of the pets required for these strategies I would recommend capturing and leveling to 25 anyway, and they are mostly easy to obtain. If you want to beat every trainer just once for the Taming Draenor
achievement however, it might make sense to look at the alternatives provided.
Below table lists the pets used for my main strategies. If you have all of them, you will have an easy time beating these trainers:
The list of required pets can sadly not be displayed right now due to updates Blizzard is making on the armory.
A new version of the tables will be added as soon as possible.