How do you you say happy birthday in japanese?

You may say '(O)tanjoubi omedetou.'
お誕生日おめでとうございます => 'Otanjoubi omedetou gozaimasu' is polite and 誕生日おめでとう => 'Tanjoubi omedetou' is very casual/informal way to say 'happy birthday' in Japanese.
Tanjo-bi omedeto!