Someone has died, and you're reaching out now to the surviving family members.
Reflect on these ideas before you say or do anything...
(1). Your presence will mean more than your words. Just be there for them. Drive to their house, give them a hug or handshake, and spend some time with them. Don't wear out your welcome by staying too long or saying too much, but do show them you care by being there for an appropriate amount of time.
(2). Do something for them. Make them a salad. Buy them a box of chicken. Fix them a gallon of sweet tea. Mow their front lawn. Wash their dishes that are in their sink. Vacuum their living room. I think you get the point. Acts of kindness will mean the world at a time like this.
(3). Respect their right to grieve in their own way. If they need to cry, let them cry. If they get mad and cuss, just quietly stand there and let them say what they need to say in that moment. If they hold their emotions inside and express very little feeling, let them handle matters privately without pushing them to pour out their heart to you. What I'm saying is, let folks grieve in their own way. Remember we all grieve in different ways, and that's ok.
(4). Do not say "If you need anything, just let me know." That puts pressure on them to make requests that they may not feel comfortable making. If you want to help them, just go ahead and help them. Or you can say this: "I want to help you. What is your greatest need right now?"
(5). Avoid using this cliche about the deceased: "Well, he's in a better place now." While it is a true statement, and it is good to know, that grieving family still misses the one who died. They are hurting because that special someone who died is no longer with them. I've had people tell me they got tired of hearing this phrase used over and over when their loved one died, and I can see why.
(6). Stay away from the phrase "I understand." You're not that grieving person. You're not in their skin. Their feelings are unique. You understand how you may would feel if you lost someone, but you do not understand how they feel. Please do not use this phrase.
In summary, just remember this: Show up, give them a handshake or a hug, tell them you care about them, do something for them if you can, and then just let them respond in their own way. They don't need sermons and cliches at that particular moment. Not at all. They just need your presence, love, and prayers more than anything.