Health and mental health are examples of pools. Used up by damage, and rolled under for tests, or rolled over for actions used to increase pools, like a healing spell. Another example would be a fear pool for a horror type game.
Creating pools should be as simple as anything else in the Fugue system is, so the rule is 2d6+attribute=pool. Take the fear example, 2d6+mind=fear pool.
You may also of course use 1d6+attribute for pools used to augment an action.
A western game might include a fast draw pool, 1d6+body, each time a the character gets into a situation where a fast draw could happen they may add to their roll a bonus equal to the amount of fast draw pool that they use.
Replenishing pools should require a timed action, like resting or brewing more potions… etc…