"I am really happy" means "I am very happy" or "I am so happy." You are describing how happy, excited, nervous, etc. you are. "I am REALLY _______!" This version is what you will most commonly use. "I really am happy" is when you are convicing someone it's true. For example, your girlfriend thinks you are not happy with her ... then you tell her "I really AM happy." (..."it's true!.."). If that is too confusing, then just use"I am really...." because it works for both!