First, it is helpful to remember if you are in a line at a funeral home, you are already doing the most important gesture of caring. You may be uncomfortable, but you are there.
Ok, but what do you say when you are face-to-face with the grieving person? I have found it helpful to follow these basics:
We need to remember that the grieving people are under a lot of stress and may not remember who you are. They may wonder, “where do I know this person from? Is she from work or church or did I go on a mission trip with her?” For example, to the son of the deceased woman I would say, “Hi, (I might hold his hand) my name is Karen Mulder and your mother Margie and I were roommates in college.” Now I have done 3 things that may be helpful to the son:
(1) Introduced myself (2) Told my connection to his mother (3) I used the deceased person’s name
Then I could (4) express simply my sympathy by saying, “I am so sorry about the death of your mother.” Or, “I can’t even imagine how sad (or lonely or devastated) you must be.”
And then if it seems appropriate and natural I would (5) include an incident, story or an admirable quality about the deceased person. I might say, “Your mother was a very kind and considerate person. I remember one time when when I failed an important exam and I was devastated. Your mom dropped what she was doing and took me out for a huge hot fudge sundae. I know lots of other fun stories about your mom; so call me sometime and we will get together for coffee and I will tell you some great stories.”
If you do not know the deceased, look at the pictures of her or his life display. Then you could mention something you saw in the pictures or maybe you have a question. “I saw in the pictures Margie helping in a primitive looking hospital. Where was she and what was she doing?” That may generate some conversation and give the son a chance to tell about his mothers work in developing countries.