I'm at a loss for people who have suffered a loss

Growing up, I have been surrounded by people who are amazing at helping others when they need it.  My mother is the most incredible person in a crisis.  She can keep a level head and look at things very logically.  My mom is a very busy woman, and she likes it that way.  The greatest thing about her, though, is that she will drop everything that she has going on if someone in her family needs help.  She is amazing and she has helped me through some really tough times!
My Grandmother is another example of someone who is amazing at service.  Growing up I would always end up accompanying her to visit someone in the hospital, someone who is sick or just someone that she was thinking about and decided to take a meal to, just because.  Whenever someone would have something happen in their lives, instead of saying "If you need anything, just let me know", she would simply do things.  She would take their laundry and do it for them, or clean their house, or show up randomly with food, or take them to run errands.
These amazing women have taught me so much about service, and because I am such a loyal person, if someone that I really care about needs something, I am always there.  I make sure that I help my family and friends whenever I can because it is my way of showing them I love them.
Right now I am having a bit of a hard time.  There is a person in my church whom I have always admired and her mother has just passed away suddenly.  I have never been in a position where someone who I don't know really well, but still care about has needed help.  What do I do?  What do YOU do???  Do I offer the simple non-commital phrase of "If you need anything, just let me know."?  Do I bring her a meal?  Right now I am baking her a bunch of snacks and quick foods to have on hand as her family comes and stays with her, but is there anything else that I can do?  I tried calling her this morning, but she is having a really hard time and couldn't really talk.  What would YOU do???
I would love some ideas because I am truly at a loss here.