Learn Italian: Non sei felice. - You are not happy.

In Italian, the negative word non always goes directly before the verb it is negating. While in English we put "not" after the verb ("You are not"), Italian does the opposite. You literally say "Not (you) are" (Non sei).

Where is the word for "you" in this sentence?

The word for "you" is tu, but it is left out here. Because the verb sei is only ever used with "you", the subject is already obvious. Saying Tu non sei felice is perfectly fine, but dropping the tu is much more common and natural in Italian.

Would felice change to felica or felico depending on whether I am talking to a man or a woman?

No, it stays exactly the same! While many Italian adjectives change to end in -o for masculine and -a for feminine, adjectives that naturally end in -e in the singular dictionary form, like felice (happy), are used for both men and women.