Learn the Spanish word for "to be." While there are actually two words for "to be" --- "ser" and "estar" --- the only one you need is "estar," because this is the word used to express temporary states. Emotions are considered temporary states because they change from moment to moment.
Conjugate "estar" to mean "I am." To do this, you simple say, "estoy." If you want to express how you feel, say "estoy" followed by the adjective for the emotion.
Here are some of the principal emotions that you may need to express:
Estoy alegre. = I'm happy.
Estoy emocionado. = I'm excited.
Estoy enojado. = I'm angry.
Estoy feliz. = I'm happy.
Estoy nervioso. = I'm nervous.
Estoy preocupado. = I'm worried.
Estoy triste. = I'm sad.
Note that if you are a woman, you must adjust the above emotions from masculine to feminine --- change the letter "o" at the end of a word to an "a." That's because adjectives in Spanish differentiate between the sexes.
For women the emotions that change are:
Estoy emocionada.
Estoy enojada.
Estoy nerviosa.
Estoy preocupada.
Note that the other emotions do not change since they don't end in "o." A woman would still say, "Estoy triste," to say that she is sad.