Write the story completely from your point of view, or from the point of view of the character who is narrating the story. Write about your actions, your observations and your thoughts.
Speculate on other characters' thoughts and feelings from your perspective. By focusing on more than just actions that you can see, you can build more character depth with your other characters.
Use hearsay to tell other parts of the story. If events occur when you are not present, you can use another character's telling of the story to you.
Be wrong sometimes. Since you're writing from the point of view of one person, it's realistic for that person to sometimes make a wrong impression or assume something that isn't true. Use "being wrong sometimes" as a way to add suspenseful elements to your story.