Experience (and thus advancement) is gained by literally doing what you want to get better at, meaning you get better at swimming by swimming, get more accurate with guns by shooting with them, get better at preparing food by cooking, etc.
Alternate names: Character advancement: Literal experience, Learn by doing
The first video game about Experience: Literal was released in 1984.
At the most extreme point, games in this category don't have anything akin to the classic level system used by the oldest RPGs (and those that mimic their system) out there.
This also means you don't gain experience from doing quests either, besides what ever skills you used to finish it but that's no different from any other use of skills and the questing should not give any boosts to it lest it be in the realm of regular experience system.