Use the word "feliz" to mean happy. This is the most common translation of the word "happy." You can say "estoy feliz," meaning, "I am happy (now)." If you say "soy feliz," it means "I am a happy person." This implies you are almost always happy.
Say "estoy alegre" if something makes you happy. "Alegre" is another word implying "happy." If you found out some news that makes you happy, you could say, "me alegro."
Use the word "contento" to describe feeling content. This word is used more frequently in Spanish than the word "content" is used in English. Use "contento" for men, "contenta" for women and "estoy contento(a)" to say "I am happy."
Use the correct phrases to wish someone a happy birthday or Merry Christmas. "Feliz cumpleaños" means happy birthday while "feliz Navidad" means merry Christmas.