From context, mainly.
ESTAR
I'm happy that my team won.
I'm happy due to my team's victory.
I'm happy because my team won
SER
I'm a happy person - ser
The second is very clear and it is usually used with "person" because you are referring to a characteristic and not a temporary state. Also, note the use of the article "a" = sou feliz, sou uma pessoa feliz.