The name can give clues about the character. It can suggest the generation or historical setting. You don't see many teenagers named Mildred nowadays, but that name may be perfect for someone born in the 20s. The Social Security website has a database of name popularity by year.
Nicknames can also reveal details about the character. It can say something about how he views himself or how other characters view him. For example, his mom calls him Billy because she still sees him as her little boy. He introduces himself as William, but his friends all call him Will.
When describing a character's appearance, forego details into things such as hair and eye color (unless these are particularly unique). Instead, focus on things that the character can control about her own appearance--hairstyle, clothes, and the like. Zoom in on a small detail or two that reveals the most about the character's personality.
Again, keep the focus on what the character can control. What do the furnishings, decorations, or refrigerator contents tell us about your main character's personality? Mixing a few details with the action give the reader a sense of the character's environment without slowing the pace.
What a person says and how she says it gives clues about her character because different people express the same thing in different ways. A light splattering of dialect adds to the character, but don't go overboard with it. The readers can pick up on the dialect without the author misspelling every other word.
The character's actions key the reader into his personality. Creating actions that contradict his words shows depth. Like in the Hunger Games when Peeta says he doesn't want to be a piece in their game but plays along to stay alive.
Action alone doesn't show the character's true motivation. Go deeper into the protagonist's point of view to show what he is thinking. Thoughts that contrast with his dialogue and actions give the reader insight. For example, Hamlet pretends to act crazy (when his soliloquies show otherwise) in order to investigate the murder of his father.
The reactions between two characters tell something about each of them and their relationship. What does it say about a character when others look up to her? Or if a trustworthy person dislikes her? How other characters react to the protagonist informs the reader.
Readers learn about the character through his perception of the environment. Let's say the protagonist encounters a shady grove of trees. If he sees gloomy shadows, then perhaps he is a negative person. If he sees a welcomed relief from the sun, then perhaps he has a positive outlook. The shadows haven't changed, but how your character perceives them says something about his personality. Perception can also reflect his current emotional state.
Rather than naming the emotions, it is important to make the reader feel them. At the same time, don't pile on the metaphors. Use external signs such as blushing and blinking, or use internal changes, like a tight throat or shortness of breath. The character could also have a brief memory flash or other thoughts to indicate her emotions.