The most asked question in Battleheart Legacy is this "How can I become a Ranger, Paladin, Knight, Wizard, Rogue, Ninja, Bard, Necromancer, Witch, Barbarian, Battlemage or Monk".
The answer can be foun here. Check out below where are the exact lovation of the trainer for each class.
Ranger - available from the start of the game
Paladin - available from the start of the game
Knight - available from the start of the game
Wizard - available from the start of the game
Rogue - available from the start of the game
Ninja - You get a random encounter where you must side with the female ninja and help her defeat the guards. She will then tell you to visit the ninja hideout. Once you visit the hideout and talk to her again a whole troop of guards charges in. Yet again you must side with the ninjas and assist in defeating the guards. Once this is done you are able to learn ninja skills.
Bard - located in the Capital's tavern (Eston).
Necromancer - Go to the Mage tower and accept the request to help the Mage their with his class. He will send you on a quest to get a spider gland. Clear the Crypt directly north-east of the Mage Tower to find the Skull of Necromancy. You don't need to get the spider gland anymore. With the Skull in your possession, return to the Mage tower and you will encounter the Necromancer trainer in the headmasters chamber.
Witch - located in a forest that a drunk tells you about. Once you find her, she asks you to get a Book from town. Go to the town bar, and you're guided to a Dungeon. Enter the Dungeon and find the book in a chest (don't open it when prompted!). Take it to the Witch and she'll be glad you didn't open her book  She'll offer to train you.
Barbarian - Talk to a NPC in the Academy in the Capital who will mention 'the Ox' Barbarian is to the east. Go to the camp and speak with him. He will challenge you to defeat a frost wyrm. Do so and bring back the tooth to unlock this class.
Battlemage - For battlemage to appear you have to get quest from royal guard barracks in capital which sends you to the desert outpost otherwise he will not be there. You go to the fugitive camp at the northwest of the map (level 7 map). Run all the way to the last room (if you are low level and just want to unlock the Yclass, you can ignore all the fights), and you will encounter an event where some dude that can imbue his sword with fire kills another mage. You talk to him thinking "awesome, I am gonna learn this" but nope, he won't actually teaches you there (funny conversation). After that, you have no choice but to leave the map with the treasure and a sad face. Then you try to run around the map again and you will encounter him once more. Help him fight the group of bandits and he will teach you the way of battle mage back in the city.
Monk - In the capital pub. When you enter for the first time you will notice a cutscene. Talk to the lady after she beats up the shady man. She will challenge you to a fight (unequip your weapon as it is a fist fight challenge) and then offer to train you in the way of the monk.