The best is to just listen to the person. Paraphrase a little so they know you are hearing and understanding them. Most people just want to vent and feel understood.
I usually try to show empathy, I’ll tell an example of a similar experience I’ve been through to demonstrate my understanding, because this helps me when others do that for me, but it can backfire! Some people see it as competing or making it about me instead of them. I learned that the hard way. You need to know your audience.
Sometimes I might try to give them facts that I think will reduce their fears, but that only works with some people, and it depends what they are worried about.
Mostly, I think we want to help guide the person out of their discomfort, but sometimes letting them be uncomfortable is the best thing we can do for them.
Someone very upset by loss I usually match their upset to some extent. If they cry I’m likely going to tear up too.
Part of my reaction depends on my relationship. If my husband was anxious about something I would cuddle with him. Physical touch brings down our heart rate and blood pressure, so there is real reason to think it’s effective, but mostly it is just my natural response.
When people are very emotional all the time about so many things it’s hard to watch them torture themselves. I completely understand feeling anxious and out of control with fear, but I also thankfully was able to work my way out of that feeling in many cases, and so sometimes I try to give advice on that. People helped me with it. The person has to believe they can handle things with less emotion though, most people who are highly emotional don’t believe it. They don’t believe they can change their brain. I don’t doubt that some brains are more hard wired than others.