Thousand Streams and Dreamweaver port have all trainers
How do I learn skills? You don't learn skills naturally by leveling up in this game that just unlocks them. You still have Mabinogi Gold to go the trainer of your class in town.
The towns that have skill trainers for your class are the 6 big towns and some of the towns you visit before level 20. Note that Archosaur, Thousand Streams and Dreamweaver port have all trainers, not just one race.
To learn skills, you need money and spirit, and sometimes, the required level of the previous skill. Also, some skills require you to level up your Cultivation level.
To do this, finish the Spiritual Cultivation quests, they start with an automatic pop-up to send you to an NPC who starts the actual quest.
They're the yellow-named quests, you can't really miss them. Finish one and your Cultivation will go up, allowing you to learn more skills.
How do I teach my Pet skills? For land and air monsters, visit Mrs. Zoologist in Southeast Archosaur, she sells skill books and upgrade skill books for your pet.
Use them at any Pet NPC by selecting "Learn Pet Skill". For water monsters, visit Mr. Zoologist, underwater in East Archosaur.