I got most of my Style Gems* from Deconstruction. However the Armorers and Blacksmiths and Clothiers and Wood dudes sell them. They can also be found in various containers in the game, in town they will be stolen. You can use those to craft, but you can also launder them if you want to level the Legerdemain Skill.

Learning new Styles is done with Motif Books, you find these in Furniture in town, furniture and most other containers in the world, and you can buy them in Guild Kiosks. Again, in town ones will probably be stealing them, but you can read them to learn the skill just the same.


*Trait Gems and Refined Materials come from this too.