Many people hesitate to offer comfort to those who are grieving because they think they don't know what to say and are afraid of saying "the wrong thing." You are not expected to - nor can you (unfortunately) - "fix it". Don't let this fear ultimatey prevent you from saying anything at all or keep you from offering what the grieving person needs most - YOU!
So, here are some guaranteed, sure-fire, no fail, could-never-be-the-wrong thing suggestions:
Open your arms. Hug person. Listen. Repeat.
I'm so sorry for your loss; I don't know what to say. How can I support you?