1. "My heart is with you."
It's short, sweet, heartfelt, and always welcomed.
2. "Please know that I'm here for you."
It never hurts to remind someone in pain of your friendship, no matter how close you are.
3. "You're in my thoughts and prayers."
Even people who aren't religious are unlikely to be offended if they know you're sincere (or leave off the "prayers" if you think they might be).
4. "Remember you can call me at any hour."
Alternately, be specific: "You know I'm always up till midnight." Or, "It's never too early in the morning to call." You might ask when the hardest time for the person is and check in with them at that time.
5. "One of my favorite memories is..."
Share your favorite memory of the person who died. Don't worry that you'll make the bereaved person think about the loved one by bringing up positive reminisces; you can rest assured he or she is always in mind already.
6. "I don't know what to say."
Admitting you're tongue-tied about offering condolences is better than falling back on a platitude.
7. "I can't imagine what you're going through."
Candor when you give condolence beats comparing the death with your own stories of loss.
8. "Would you like to talk about it? I'm listening."
Provide a gentle opening for the person to share turbulent emotions, fi desired.
9. "How are you feeling - - really?"
A more pointed invitation to unload may be welcomed by some: just don't press.
10. "I've brought you a meal to eat or freeze; it's in disposable containers so you don't so you don't have to return anything." or "I would like to take the kids for the afternoon on... "
Better than asking, "How can I help?" is to step in with concrete help.