A character earns renown by completing missions or quests that serve an organization’s interests or involve the organization directly. You award renown at your discretion as characters complete these missions or quests, typically at the same time you award experience points.
Advancing an organization’s interests increases a character’s renown within that organization by 1. Completing a mission specifically assigned by that organization, or which directly benefits the organization, increases the character’s renown by 2 instead.
For example, characters with connections to the noble Order of the Gauntlet complete a mission in which they free a town from the tyranny of a blue dragon. Because the order likes to punish evildoers, you might increase each character’s renown within the order by 1. Conversely, if killing the dragon was a mission given to the adventurers by a senior member of the order, completing the task might instead increase each character’s renown by 2, showing the adventurers as effective allies.
Meanwhile, the party’s rogue might have looted a box of rare poisons from the dragon’s hoard and sold it to a fence who is secretly a Zhentarim agent. You might increase the rogue’s renown within the Zhentarim by 2 since this action directly increased that group’s power and wealth, even though the task was not assigned by an agent of the Zhentarim.