There's a good lesson to be learned from the book "Curious George Goes to the Hospital" by Margret and H.A. Rey. I remember this lesson from reading the book when I was a kid.
In the book, George swallows a puzzle piece and doesn't feel well. The Man In The Yellow Hat takes him to a hospital so they can figure out what's wrong. This is the page that I recall:
I remember being struck by the fact that the author didn't tell you explicitly that George felt scared. Instead, the author describes an action ("George held his big rubber ball tight as they walked up the hospital steps") that creates the idea in your mind that George is scared.
That is such a great lesson in how to write: give your characters actions and reactions that clue the reader (or viewer) into how they're thinking and feeling. You feel the impact of a character's emotions much more powerfully when you perceive them in your mind this way, as opposed to a character just coming out and saying, "I'm scared".
Saying "I'm scared" is also not very realistic behavior for a character. For a variety of reasons, people rarely come right out and say "I'm scared" when they're scared. That goes for every other emotion as well. Humans are very complex, and our feelings are complex too. Most of the time people aren't really cognizant of exactly what they're feeling, and why, and even if they were, they probably couldn't articulate it. Also, most people tend to hide their emotions pretty well (this is different from person to person and from culture to culture, but it's a general truth). So when a character uses dialogue to announce what emotion they're feeling in a movie or TV show, it never feels real to me and it sure isn't very satisfying. And when a character does that, I tend to think they're lying, anyway. Think about it: in your life, have you ever had a reason to tell someone else that you're feeling happy at that moment? Or sad? I haven't. I'm not sure why anyone would be interested in a running commentary of my emotions. If I'm feeling happy, I'm just going to experience that feeling....I'm not sure why I would announce it to anyone. The same goes for every other emotion.
That's why if a character in a movie ever does announce that they're happy (or sad, or whatever), I always assume that's a lie that they're telling to cover up what they're really feeling (and then I'll try to figure out what they're really feeling, and why they're lying about it).
So for those reasons, it always seems like really poor writing to me when a character says out loud what they're feeling, and what they're saying is actually the emotion that they're feeling.
When you're writing anything, getting the audience inside the head of the characters and letting the audience know what they're feeling and thinking is one of the most (if not THE most) important aspects to communicate. So, if we can't have characters tell us what they're feeling, how do we make it clear to the viewer?
Well, because humans are so good at hiding their emotions, we humans have gotten good at reading the tiny clues people show and inferring their emotions from those little hints. So, just like in the Curious George example, use your character's actions and reactions to give the audience insight into the mindset of your character as they react to the events unfolding around them.
Sometimes that means giving your character reactions that are universally obvious (like George gripping his ball tighter to show that he's afraid). Or sometimes it involves setting up that your character has a certain behavior that he does when he's feeling a specific emotion, and then when your audience sees the character do that certain behavior, they know what he's thinking or feeling (for example, in Michael Bay's "The Island", there's a set up that Ewan McGregor's character smiles in a certain way when he's lying, and that serves as a setup for a plot point later).
The point is this: what a character does in a story - the actions he or she takes, and the reactions he or she has to events in the story - should tell us about who they are and what they're feeling. Not speeches where they announce what they're feeling.
As a writer (or storyboard artist, animator, comic artist, etc.), it's imperative that you know what your character is thinking and feeling at all times and why. If you don't know these things, then you can't communicate it to the audience, and then the story just becomes a series of meaningless events. Nobody watching it will know what they're supposed to be feeling or what they're supposed to think about the story you're telling. So the first step before you can communicate those feelings to the audience is making sure that you know the emotions of your characters (and that those emotions make sense...but that's a whole other topic).