Basically, you have to narratively justify every stat increase (and create a new resolvable trait based on it), but you can choose to increase your stat at any time. Naturally, the best move is to wait until you need to make an important roll to increase a stat, so it happens in the middle of action.

One thing about the game is that if a character has a low stat, that just means it *seems* low. To put it in DnD terms, a low-int character might appear unintelligent, until the dramatic reveal that they were secretly smart the whole time.