お誕生日 おめでとうごうざいます!
おたんじょうび おめでとうごうざいます!
o-tanjyoubi omedetou gouzaimasu!
Happy Birthday!
PS: recognize the last character in "tanjyoubi?" It's the sun character, for day!
The second character is worth remembering as well. It's 生, which means life, raw, birth, and a host of other related ideas.
生 - SEI, SHOU (JYOU), nama, i-kiru, u-mu, u-mareru, ha-eru
That's a lot of readings! The most important ones are "SEI," which appears in words like gaku-SEI (student), SEI-katsu (life), and dou-kyuu-SEI (classmate -- see gozen's previous post on jukugo)
nama, which means "raw," or most importantly, beer off the tap (just walk into the bar and ask for a "nama biiru"
i-kiru, which literally means "to live" in the sense of "exist." I believe this is the "ikiru" you can hear at the beginning of Kenshin OVA1 "Shinta, ikite...ikite," (Shinta, live!) but I'm going from memory on that one.
and "u-mareru," which means "to be born" (amerika ni umaremashita - i was born in the USA)
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for extra info: u-mu means "to bear," but it's a transitive verb which you probably won't use in everyday conversation much. It shares readings but not usage with 産む (umu), which is the "u-mu" used in sentences like "I bore a child."
ha-eru means to grow (like, there are flowers growing behind my house).
The character for TAN is a more difficult, middle school character. It doesn't appear in many words besides "tanjyoubi" so you can get away with not really knowing it -- when you see some character + 生日 just remember it's probably TAN. It means "born," but I believe always appears in those elusive "jukugo" kanji compounds gozen was talking about a few days ago.