“The only way of expressing emotion in the form of art is by finding an "objective correlative"; in other words, a set of objects, a situation, a chain of events which shall be the formula of that particular emotion; such that when the external facts, which must terminate in sensory experience, are given, the emotion is immediately evoked.”
We've all heard that, but HOW IS IT DONE?
When does tell become show?
George was nervous. (definitely telling)
George's heart pounded. (Sort of showing, but still mostly telling. I'm telling you his heart pounded. Why is that different from telling you he was nervous? It's even more ambiguous. Is he scared or excited?)
"Relax. This won't hurt a bit." The dentist held the drill poised over George's face. The drill motor whirred. George stared at the yellow-brown stain on the ceiling and wished he had paid for better dental insurance.
Now I don't need to tell you that George is nervous or that his heart is pounding. I've put you in his head and you're seeing things through his current emotional filter. He's noticing the drill in front of his nose, the sound of the motor, the stained ceiling. How does he feel? Mommy, get me out of this chair!
This is the objective correlative. You've got to choose what your characters notice based on how the characters are feeling at the time, then relate those things to the reader. Paint an emotional picture with objects, situations, and events. Give your reader the facts, and let the emotion come out on its own.
Here's your writing exercise. Get your notebook and write down four emotional states, spacing them out on the page. Then walk into another room in your house. Any room you like. Describe that room through each of your four emotional filters.