Players receive two traits during character creation which they can choose. GMs can award players with more traits over the course of gameplay, and this is completely up to GM discretion. Some traits specify they cannot be taken during character creation, and must be taken during gameplay.
Prerequisite Traits: Some traits are required to be taken at character creation in order to apply to certain classes. They are able to acquire traits after character creation at the behest of the GM, however ways outside of character creation that allow them to acquire new traits (such as a talent) cannot choose these.
For example, in order to apply to Divine Inspiration you must take it during character creation. If you don't, you'll need to go through training with a Priest to acquire it.
Negative Traits: Some traits affect your character in negative ways. "Why take them?" some may ask. These negative traits will either include a benefit (such as a situational bonus to a skill) or awarding the character TP if the trait comes into play. The latter is used more often in the case of traits that offer no statistical benefit.
History Traits: History traits are used used as part of the character's backstory - representing a part of their backstory which affected them in a major way or has long-reaching implications. These traits can only be taken during character creation, and shouldn't be "awarded" by the GM due to their nature as backstories.
Awarded Traits: Sometimes a GM may award a player with a trait free if they feel it fits the character. These traits should always be traits which are more personality traits (Addict or Philanderer) which can crop up mid-game rather than birth effects or things required at character creation (such as Child of the Moon).