There are four main skills:

Your ability to fight off enemies: These skills can be built up by training at the Grand Entertainment Hall with an NPC named Tallawah.

Your perception ability, which will allow you see better items while out on a job, and identity certain items found: This skill can be enhanced at the City Hall with an NPC named Erica.

Your arcane ability, which is used to see spirits and other creatures, and to transmute certain items into others to sell: This skill can be bolstered at the Crimson Scale Club with an NPC named Mistress Whyte.

Your lockpicking ability, which will be needed to unlock various doors and chests: This skill can be mastered with an NPC at the church named Jade.

You can also increase your Max Health, which will help you survive various assaults by enemies by training with an NPC named Qiang at the Second Hand Mart.