Storytelling through action and dialogue

The following quote from Akira Kurosawa has been used in an article on thestorydepartment.com:

It’s easy to explain the psychological state of a character at a particular moment, but it’s very difficult to describe it through the delicate nuances of action and dialogue. Yet it is not impossible. A great deal about this can be learned from the study of the great plays, and I believe the “hard-boiled” detective novels can also be very instructive.

Write a story about a character who earns the trust of another character through their integrity, told through action and dialogue (that is, no 'internal dialogue,' description of character thoughts and feelings, description of memories and backstory etc).