The two main words here are:

kufurahi (verb) "to become happy"
furaha (noun) "happiness"

Because kufurahi is one of these verbs of "becoming", i.e. a change of state, to talk about the static state, you use the perfect:

Nimefurahi. = I am happy. = I have become happy.

You can also use the noun to get the same meaning. Just use it with the equivalent of "have". To have happiness = to be happy.

Nina furaha = I am happy. = I have happiness.

Other examples:
watu wenye furaha = happy people = people with happiness
watu waliofurahi = happy people = people who became happy
tembea kwa furaha = walk happily = walk with happiness