To say "happy" in Spanish, you can say "feliz" or "contento," though "contento" implies a happiness deriving from "satisfaction," whereas "feliz" is just pure happiness.
If you want to say "I am happy," you can say "Yo estoy/soy feliz."
--> Just a small note on "soy" vs "estoy":
>"Soy" = Implies a more permanent state, usually used if you're "being" something; i.e. "Yo soy feliz" = I am happy (most of the time)
>"Estoy" = Implies a temporary state, in the moment; "Yo estoy feliz" = You are happy (does not mean you are always or usually happy, it just means that something happened which made you feel happy)