Formal:
* Я счастлив(а). (Ya schastliv(a).) - This is the most literal translation and is appropriate in formal settings.
Informal:
* Я рад(а). (Ya rad(a).) - This is a more common and informal way to say "I am happy." It can be used with friends and family.
* Я доволен(льна). (Ya dovol'en(l'na).) - This means "I am satisfied" and can also be used to express happiness.
* Мне хорошо. (Mne khorosho.) - This literally means "I feel good" and is a more general way of saying "I am happy."
For specific situations:
* Я очень рад(а) тебя видеть! (Ya ochen' rad(a) tebya videt!) - "I am very happy to see you!"
* Я рад(а) за тебя! (Ya rad(a) za tebya!) - "I am happy for you!"
Remember to use the correct gender ending for the adjective "happy" depending on your gender. "Счастлив" (schastliv) is for males, "счастлива" (schastliva) is for females, and "счастлив" can be used for a group of people.