The Wikipedia explanations:
Faith:=
To have faith in ones spouse that he/she will keep a promise of commitment
To have faith that the world will someday be peaceful
To have faith in a person to pay you back
Belief:=
Belief is the psychological state in which an individual is convinced of the truth of a proposition. Like the related concepts truth, knowledge, and wisdom, there is no precise definition of belief on which scholars agree, but rather numerous theories and continued debate about the nature of belief.
Trust:=
Trust does not need to involve belief in the good character, vices, or morals of the other party. Persons engaged in a criminal activity usually trust each other to some extent. Also trust does not need to include an action that you and the other party are mutually engaged in. Trust is a prediction of reliance on an action, based on what a party knows about the other party. Trust is a statement about what is otherwise unknown -- for example, because it is far away, cannot be verified, or is in the future.