Trainers in Dragon Age 3: Inquisition are NPCs who teach the Inquisitor their chosen Specialization.
"The best of the best have been summoned. Training with these "specialists" will ensure the Inquisitor's abilities remain at their height."
Trainers can be found at Skyhold after the Inquisitor has completed the Specializations for the Inquisitor operation at the War Table. Once this mission is completed, the trainers for the various specializations will appear, offering individual missions to unlock one of the specializations.
Once the Inquisitor has completed the War Table operation Specializations for the Inquisitor, three trainers relevant to the Inquisitor's class will appear in Skyhold. Speaking to these trainers will make available the below quests, and completing one of these quests unlocks the relevant Specialization. The Inquisitor may only choose one of the specializations, so it's best to speak to each trainer before making your choice.
Warrior Specialization Quests:
Mage Specialization Quests: