Basics about styles (minus Brave and Alchemy) and weapon specific arts. They added some new weapon-specific arts for MHXX as well. Those dont have descriptions here, but most are self explanatory.
Some arts, usually weapon-specific ones, are upgradeable by completing certain quests.
You can find the style and arts menu here in your house box:
This is the style menu, where you can change your hunting style. From top to bottom: Guild, Striker, Aerial, Adept/Bushido, Brave, and Alchemy.
Equipping a style will bring you to the Arts menu, where you'll see 1 to 3 available slots that you can place arts in (number depends on the style you use).
You want to kinda limit yourself to using weapon-specific ones or the Absolute Evasion arts, the rest are pretty throwaway. The last few arts in the menus are always weapon-specific, and the first art is always Absolute Evasion. There is another evasion art, Absolute Readiness, which can be easily unlocked by doing a specific quest. It will then appear right below the Absolute Evasion art.
Both evasion arts charge up quickly, so they're very useful.