心からお悔やみ申し上げます （こころから　おくやみ　もうし　あげます） . Please accept condolences from the bottom of my heart. Here is a good website for different phrases to say according to different circumstances you'd give condolences (and what not to say on the bottom): http://www.arkbell-ceremony.com/sanretsu/05/word.php Also here's another one explaining the above phrase a little more: http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q11102626296 You could say what Daniel said above, but add この度（この度・このたび）は in front of it as the second link (and my dictionary) suggest or この度はまことにご愁傷さまです。(You truly have my sympathy/You have my sincere condolences) I am not sure if there is a less formal way to do it, but the second link has these two sentences which seem a little less formal that the above. 「哀悼の意を表します」(あいとうの　いを　あらわします I would like to express my deepest symphathies.) 「哀悼の誠を捧げます」（あいとうの　まこと　を　ささげます I truly offer you my condolences.)

ご愁傷(しゅうしょう)さまです。 or ご愁傷さま。