1. We Respond by sharing the Truth of the Gospel -- If we really understand the doctrines of heaven and hell, God and sin, and what Jesus came to do on the cross, we should be motivated by love to share the Gospel with people who are running head-long for hell. We don't look for conversions to add to our Christian belt loop, nor should we get angry if someone rejects us or has a hard time believing the Truth. We simply need to respond in love by telling them the good news of Jesus life-saving news, and their need to respond in repentance and belief.
2. We Respond with Compassion -- I think as Christians we downplay death if the person was a Christian, saying we should celebrate because he's in heaven, and if non-christians die, we often second guess and wonder if he/she was saved at the 11th hour. Instead, I think we should respond in two ways. One is to enter in with those who are grieving. Jesus wept when Lazurus died, even when He knew He was going to raise him from the dead. Why? Because death is an unnatural thing that was caused by human sin, and it absolutely decimates us. (I'm not saying you can't celebrate that the person is in heaven, but it's ok to grieve, and it's ok to let other people grieve.)
The other is to consider how to care for those affected most by the death, in hopes of sharing the Gospel (both to believers and non-believers). The Gospel is the most compassionate thing we can offer at a time of grief, as Jesus promises one day there will be no grief, no more tears, no more suffering, and no more death. But we must aim to share this truth sensitively, lovingly, and genuinely. So don't just drop a Gospel Bomb, but find out how you can make meals for a family that's grieving, offer to help with the details, give people space if they need space. Understand how to love them, in hopes of moving the proverbial ball down the field.
3. We Respond with Hope -- One of our greatest weapons as Christians is our reason for Hope. As life falls apart around us, we can stand and say, "one day, life isn't going to be this way!" Not convinced? Check out Revelation 21. I'm often tempted to believe that when I die, all this Christian stuff was for naught, that I was never really saved, and either there is no God, or God isn't who I thought He was and He wouldn't ever tolerate a guy like me. But the hope of the Truth of the Gospel is that if you trust in Christ, you have eternal life with God. Your life has been purchased by Jesus' blood! There's no bigger price that can be paid, God spared no expense! If He did that, how could He change His mind and say, "you know... I thought I would save you, but you've messed up too many times." It's absurd, Jesus is sufficient to reconcile all things to Himself! (Col. 1:15-23)