depending on how excited or happy, i usually shake/flap my arms(always), rock back and forth, the faster the happier i am(i do this for the stronger emotions i think, so i usually do), jump (usually), hold my breath(most times), run around(if very happy/excited) or pace(usually/always, but i do it always anyway), cover my eyes/put my head down and put my arms over (sometimes/if I'm at a desk or table) scream (not too much, more of an internal suppressed scream) Sometimes i may not even react, i could be the happiest kid in the state and apparently look depressed, I'm not good at expressing things on the outside
a few years ago this kid in my class for two years came up to me and asked why i never smile, she'd never seen me smile. shocked, i laughed, all this time i though i looked happy, and smiley i wasn't, and that was a happy year for me
i do always do the arm or hand flap thing though, and the rocking thing, and hold my breath, i don't even notice half the time until someone asks me if i'm alright 
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"Be who you are and say what you feel because those who mind don't matter and those who matter don't mind." ~ Dr. Seuss