So, let's say that a family member or friend of yours is in crisis. Someone has died, or a child is very ill, or there's been an accident, or Russian Mafia have abducted the President's daughter.
Let me start with what you should never say. "I know how you feel." Unless you have been through the EXACT thing, you don't. In line with this, don't compare, for example, "I know how you feel. I haven't had a baby die, but in 3rd grade my cocker spaniel was hit by a car. I cried for DAYS." No.
In line with that, don't try to be helpful about the silver lining. "Well, at least you still have ONE leg!" No.
One of the things with crisis is, it is all consuming. When you're in it, nothing else matters. People in crisis often move into survival mode, where everything else is stripped down, so they can devote all their strength and mental energy to surviving. That is why it's not a good idea to ask them to call you and update you on the status of their tragedy. No. Find a relatively stable contact person, who is on the close outskirts of the situation without actually having blood on them, and get updates from them. Or if there are general updates online, work with those. People in crisis will tell you the nitty-gritty when they're ready.
Some things that are generally good to do:
Give food. Everybody has to eat, and even if there's no appetite now, at some point there will be.
Say something. "I'm so sorry" is a good start.
Give money. Crises are expensive.
Give practically; offer to babysit or clean their house. Don't say "Let me know what you need." They probably won't.
Offer an ear, when or if they're ready to talk. Often after a tragedy, you might not know what you are and aren't allowed to talk about, so let them lead. If they bring up their loved one, then don't act awkward or change the subject. Just listen.
Hug them, pray for them, and most of the time, don't offer advice. Odds are good that you don't know what you're talking about.
Ultimately, you will do some things right and some things wrong. The important thing is to be there, physically or emotionally, however the person in crisis prefers to be supported. Good luck!