How to console a friend who lost a mother or a father

"I'm very sorry for your loss. I know that you and your father were very close, so I can only imagine how you feel right now, and I wish I could be there to stand with you in your difficult times." At this point she'll probably thank you and mention things about her father, wait for her to let it out and go along with what she says, be it memories or questions or what have you, let her guide the conversation. If you are willing to help out financially, and they need it, now would be the time to make an offer of support. Close with this, "I want you to know that you're on my mind and in my heart, and that I'm here for you if you ever need anything, and even though I can't replace what you've lost, I'll always be your brother/sister no matter how far away. So if you ever feel like talking, or venting, or need a shoulder to cry on, I'm merely a thought and a phone call away."